A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Haley buys a refrigerator with the price of $\$4\,050$ on hire purchase with a down payment (in percentage) and the remaining to be paid in monthly instalments over $12$ months at a simple interest rate of $20\%$ per annum. Given that her monthly instalment is $\$324$, find Haley’s down payment in percentage of the total price.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Alex buys a TV with the price of $\$4\,000$ on hire purchase with a down payment of $10\%$ and the remaining to be paid in monthly instalments over $12$ months at a simple interest rate of $15\%$ per annum. Find Alex’s monthly instalment.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Lucas buys a personal computer on hire purchase with a down payment of $20\%$ and the remaining to be paid in monthly instalments over $24$ months at a simple interest rate of $10\%$ per annum. Given that Lucas’ monthly instalment is $\$126$, find the price of the personal computer.</span></div></li></ol>

Haley buys a refrigerator with the price of $\$4\,050$ on hire purchase with a down payment (in percentage) and the remaining to be paid in monthly instalments over $12$ months at a simple interest rate of $20\%$ per annum. Given that her monthly instalment is $\$324$, find Haley’s down payment in percentage of the total price.

Alex buys a TV with the price of $\$4\,000$ on hire purchase with a down payment of $10\%$ and the remaining to be paid in monthly instalments over $12$ months at a simple interest rate of $15\%$ per annum. Find Alex’s monthly instalment.

Lucas buys a personal computer on hire purchase with a down payment of $20\%$ and the remaining to be paid in monthly instalments over $24$ months at a simple interest rate of $10\%$ per annum. Given that Lucas’ monthly instalment is $\$126$, find the price of the personal computer.

Simple Interest

Hire Purchase and Instalments

Rate

Percentages

<p>Xiao Hao wants to deposit an amount of $\$120,000$ into a bank that pays a simple interest. He has three options of deposit plans:</p>
<p><strong>Option A</strong>: Simple interest rate of $2.75\%$ per annum. </p>
<p><strong>Option B</strong>: Simple interest rate of $2.15\%$ for the first annum, with an increment of $0.30\%$ for each of the following years, but no more than $3.05\%$. </p>
<p><strong>Option C</strong>: Simple interest rate of $2.50\%$ for the part of deposit below $\$90,000$; Simple interest rate of $3.25\%$ for the part of deposit above $\$90,000$.</p>
<ol class="roman-list"><li><div class="list-item-content"><span class="list-item-text">If Xiao Hao decides to deposit the money for $3$ years, find the total amount of interest he will receive for each option, respectively, and state which option is better in terms of the interest gained.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If Xiao Hao chooses Option A, and received a total interest of $\$13,200$, find the number of years he deposits his money.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the least number of years Xiao Hao should deposit his money for Option B to yield a higher total amount of interest than Option A.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the least amount of money one should deposit for Option C to yield a higher amount of interest annually than Option A.</span></div></li></ol>

Xiao Hao wants to deposit an amount of $\$120,000$ into a bank that pays a simple interest. He has three options of deposit plans:

**Option A**: Simple interest rate of $2.75\%$ per annum. 

**Option B**: Simple interest rate of $2.15\%$ for the first annum, with an increment of $0.30\%$ for each of the following years, but no more than $3.05\%$. 

**Option C**: Simple interest rate of $2.50\%$ for the part of deposit below $\$90,000$; Simple interest rate of $3.25\%$ for the part of deposit above $\$90,000$.

If Xiao Hao decides to deposit the money for $3$ years, find the total amount of interest he will receive for each option, respectively, and state which option is better in terms of the interest gained.

If Xiao Hao chooses Option A, and received a total interest of $\$13,200$, find the number of years he deposits his money.

Find the least number of years Xiao Hao should deposit his money for Option B to yield a higher total amount of interest than Option A.

Find the least amount of money one should deposit for Option C to yield a higher amount of interest annually than Option A.

<p>Calvin deposited $\$12 \; 000$ into each of the three banks, bank $\mathrm{A,B}$ and $\mathrm{C,}$ for&nbsp;$5$ years.</p>
<p>All three banks pay the same interest rate of $1.25\%$ per annum.  </p>
<p>Find the total amount of money he would collect if</p>
<ol class="i-list"><li><div class="list-item-paragraph">bank $\mathrm{A}$ pays simple interest.</div></li><li><div class="list-item-paragraph">bank $\mathrm{B}$ pays compound interest accumulated yearly.<br><br></div></li><li><div class="list-item-paragraph">bank $\mathrm{C}$ pays compound interest accumulated monthly.</div></li></ol>

Calvin deposited $\$12 \; 000$ into each of the three banks, bank $\mathrm{A,B}$ and $\mathrm{C,}$ for $5$ years.

All three banks pay the same interest rate of $1.25\%$ per annum.  

Find the total amount of money he would collect if

Compound Interest with Multiple Compounding Periods

Comparing Simple and Compound Interest Across Three Banks

Standard Form and Compound Interest

<p>A sum of $\$700$ is invested at simple interest and amounts to $\$952$ after $3$ years.</p>
<p>Calculate the interest rate per annum.</p>

A sum of $\$700$ is invested at simple interest and amounts to $\$952$ after $3$ years.

Calculate the Annual Interest Rate from a 3-Year Investment

<p>A sum of $\$25 \; 000$ is invested at an annual rate of $8\%$ simple interest.</p>
<p>After $9$ months, all the money is withdrew.</p>
<p>How much is this amount?</p>

A sum of $\$25 \; 000$ is invested at an annual rate of $8\%$ simple interest.

After $9$ months, all the money is withdrew.

Simple Interest on a $25,000 Investment Over 9 Months

<ol class="i-list"><li><div class="list-item-paragraph">Peter deposits $\$7680$  in a fund that pays compound interest of $3.35\%$ per annum,<br>compounded half-yearly.  <br></div><div class="list-item-paragraph">Calculate the total amount of money that Peter will have in the fund at the end of five years.</div></li><li><div class="list-item-paragraph">At the end of five years, Peter withdrew $\$6500$ from the fund and invested this<br>amount in a bank which offered simple interest rate of $4.8\%$ per annum. <br></div><div class="list-item-paragraph">Find the minimum number of full years he had to leave the money in a bank in order for it to be more than $\$12000$.</div></li></ol>

Problem involving Simple and Compound Interest

<ol class="i-list"><li><div class="list-item-paragraph">Calculate the simple interest on $\$900$ at $5\%$ per annum for&nbsp;$2$ years.</div></li><li><div class="list-item-paragraph">Calculate the simple interest of $\$3000$ for&nbsp;$3$ years $5$ months at $4\%$ per annum.</div></li></ol>

<p>Xiao Hao wants to deposit an amount of $\$120\,000$ into a bank that pays a simple interest. He has three options of deposit plans:</p>
<p><strong>Option A:</strong> Simple interest rate of $2.75\%$ per annum.</p>
<p><strong>Option B:</strong> Simple interest rate of $2.15\%$ for the first annum, with an increment of 0.30 percentage points for each of the following years, but no more than $3.05\%$.</p>
<p><strong>Option C:</strong> Simple interest rate of $2.50\%$ on the first $\$90\,000$ of the deposit; Simple interest rate of $3.25\%$ for the part of deposit above $\$90\,000$.</p>
<ol class="i-list"><li data-list-item-id="item-1760771884150-md7hjwxvs" data-list-item-path="item-1760771884150-md7hjwxvs"><div class="list-item-paragraph">If Xiao Hao decides to deposit the money for&nbsp;$3$ years, find the total amount of interest he will receive for each option, respectively, and state which option is better in terms of the interest gained.</div></li><li data-list-item-id="item-1760771885013-elyayni7i" data-list-item-path="item-1760771885013-elyayni7i"><div class="list-item-paragraph">If Xiao Hao chooses <strong>Option A</strong>, and received a total interest of $\$13\,200$, find the number of years he deposits his money.</div></li><li data-list-item-id="item-1760771885905-co8f0mby9" data-list-item-path="item-1760771885905-co8f0mby9"><div class="list-item-paragraph">Find the least number of years Xiao Hao should deposit his money for <strong>Option B</strong> to yield a higher total amount of interest than <strong>Option A</strong>.</div></li><li data-list-item-id="item-1760771887488-amodnut9x" data-list-item-path="item-1760771887488-amodnut9x"><div class="list-item-paragraph">Find the least amount of money one should deposit for <strong>Option C</strong> to yield a higher amount of interest annually than <strong>Option A</strong>.</div></li></ol>

Xiao Hao wants to deposit an amount of $\$120\,000$ into a bank that pays a simple interest. He has three options of deposit plans:

**Option A:** Simple interest rate of $2.75\%$ per annum.

**Option B:** Simple interest rate of $2.15\%$ for the first annum, with an increment of 0.30 percentage points for each of the following years, but no more than $3.05\%$.

**Option C:** Simple interest rate of $2.50\%$ on the first $\$90\,000$ of the deposit; Simple interest rate of $3.25\%$ for the part of deposit above $\$90\,000$.

Applications of Linear Equations in Real Life

IP1U8 HOT Q1

Linear Equations and Inequalities

<ol class="i-list"><li data-list-item-id="item-1760771815007-sq8s0121g" data-list-item-path="item-1760771815007-sq8s0121g"><div class="list-item-paragraph">Haley buys a refrigerator with the price of $\$4\,050$ on hire purchase with a down payment (in percentage) and the remaining to be paid in monthly instalments over $12$ months at a simple interest rate of $20\%$ per annum. Given that her monthly instalment is $\$324$, express Haley’s down payment as a percentage of the total price of the refrigerator.</div></li><li data-list-item-id="item-1760771815645-8lh56b4t6" data-list-item-path="item-1760771815645-8lh56b4t6"><div class="list-item-paragraph">Alex buys a TV with the price of $\$4\,000$ on hire purchase with a down payment of $10\%$ and the remaining to be paid in monthly instalments over $12$ months at a simple interest rate of $15\%$ per annum. Find Alex's monthly instalment.</div></li><li data-list-item-id="item-1760771816110-gukdqncbe" data-list-item-path="item-1760771816110-gukdqncbe"><div class="list-item-paragraph">Lucas buys a personal computer on hire purchase with a down payment of $20\%$ and the remaining to be paid in monthly instalments over $24$ months at a simple interest rate of $10\%$ per annum. Given that Lucas’ monthly instalment is $\$126$, find the price of the personal computer.</div></li></ol>

IP1U8 HOT Q2

<p>Thomas bought a dining table set through hire purchase. After paying the deposit, he had to pay $\$260$ per month for&nbsp;$1$ year.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">If a simple interest rate of $4\%$ was charged on the outstanding balance, what was the total interest payable?</div></li><li><div class="list-item-paragraph">If Thomas paid a deposit of $\$420$, find the cash price of the dining table set.</div></li></ol>

Thomas bought a dining table set through hire purchase. After paying the deposit, he had to pay $\$260$ per month for $1$ year.

IP1U8 Exercise Q10

<p>Mr Wong bought a TV set which was priced at $\$3885$ by hire purchase. He was required to pay a sum of $\$210$ each month for&nbsp;$1.5$ years. What was the simple interest rate per annum if he only paid $\$350$ as downpayment?</p>

Mr Wong bought a TV set which was priced at $\$3885$ by hire purchase. He was required to pay a sum of $\$210$ each month for $1.5$ years. What was the simple interest rate per annum if he only paid $\$350$ as downpayment?

IP1U8 Exercise Q9

<p>A computer can be either bought at a cash price of ${\$3460}$ or on hire purchase at a downpayment of ${\$500}$ and monthly instalments at a rate of ${12\%}$ per annum for&nbsp;${15}$ months.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the total instalment amount.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the hire purchase price.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If one is to buy the computer at the cash price, express the savings as a percentage of the cash price.</span></div></li></ol>

A computer can be either bought at a cash price of ${\$3460}$ or on hire purchase at a downpayment of ${\$500}$ and monthly instalments at a rate of ${12\%}$ per annum for ${15}$ months.

If one is to buy the computer at the cash price, express the savings as a percentage of the cash price.

IP1U8 8.3.5 Worked Example 1

<p>A refrigerator was priced at $\$4200$. Mrs Tan paid $30\%$ as downpayment and the outstanding balance in equal monthly instalments for&nbsp;$2$ years. If a simple interest rate of $4\%$ per annum was charged on the outstanding balance, find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the downpayment,</div></li><li><div class="list-item-paragraph">the monthly instalment,</div></li><li><div class="list-item-paragraph">the total hire purchase price.</div></li></ol>

A refrigerator was priced at $\$4200$. Mrs Tan paid $30\%$ as downpayment and the outstanding balance in equal monthly instalments for $2$ years. If a simple interest rate of $4\%$ per annum was charged on the outstanding balance, find

IP1U8 8.3.5 PN1 Q1

<p>A financial company lends money at an interest rate of $\$7.50$ per month for a loan of $\$1000$. Find the simple interest rate charged per annum.</p>

A financial company lends money at an interest rate of $\$7.50$ per month for a loan of $\$1000$. Find the simple interest rate charged per annum.

IP1U8 8.3.4 Worked Example 3

<p>Michael wants to invest a sum of money in a bank which offers a simple interest at $12\%$ per annum. How much does Michael have to invest if he expects to have&nbsp;$\$50\,000$ in total at the end of $3$ years? Correct your answer to the nearest thousand.</p>

Michael wants to invest a sum of money in a bank which offers a simple interest at $12\%$ per annum. How much does Michael have to invest if he expects to have $\$50\,000$ in total at the end of $3$ years? Correct your answer to the nearest thousand.

IP1U8 8.3.4 Worked Example 2

<p>Jim borrows $\$20\,000$ from a bank which charges a simple interest of $2.5\%$ per annum. Find the total interest he has to pay at the end of $2$ years.</p>

Jim borrows $\$20\,000$ from a bank which charges a simple interest of $2.5\%$ per annum. Find the total interest he has to pay at the end of $2$ years.

IP1U8 8.3.4 Worked Example 1

<p>Jane deposited $\$2000$ in a savings account that earns simple interest. After $3$ years, the total amount in her account is $\$2300$. Find the annual interest rate of the account.</p>

Jane deposited $\$2000$ in a savings account that earns simple interest. After $3$ years, the total amount in her account is $\$2300$. Find the annual interest rate of the account.

IP1U8 8.3.4 PN1 Q2

<p>John deposits his savings of $\mathrm{US}\$1000$ in a bank that pays a simple interest at $2.4\%$ per annum. If the exchange rate is $\mathrm{US}\$1$ to $\mathrm{S}\$1.40$, find the amount of Singapore dollars he will have after $3$ years.</p>

John deposits his savings of $\mathrm{US}\$1000$ in a bank that pays a simple interest at $2.4\%$ per annum. If the exchange rate is $\mathrm{US}\$1$ to $\mathrm{S}\$1.40$, find the amount of Singapore dollars he will have after $3$ years.

Currency Conversion

IP1U8 8.3.4 PN1 Q1

Ratio, Rate and Speed

<ol class="abc-list"><li><div class="list-item-paragraph">A television set is priced at $\$9500$.</div><div class="list-item-paragraph">The price is inclusive of $8\%$ Goods and Services Tax (GST).</div><div class="list-item-paragraph">Calculate the price of the television set before GST, correct to the nearest dollar.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Mr Tan bought it on a hire purchase scheme.</div><div class="list-item-paragraph">He paid a downpayment of $15\%$ and will pay the remaining in $18$ monthly instalments, at a simple interest rate of $2\%$ per year. Calculate the monthly instalment he has to pay, correct to the nearest cent.</div><p style="text-align: right;">[3]</p></li></ol>

Percentages involving Finances: GST

2023 AISS EM S1 EOY P1 Q7

<p>Sherry has an initial sum of ${\$35 000}$ which she divided into three portions $A$, $B$ and $C$.</p>
<p>She is considering placing the portions of money into three separate banks that provide returns through savings account and investment account. The following table shows the returns on savings account and investment account provided by the three banks for a period of one year:</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1759139692443-c82zf3f2oaj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NTkxMzk2OTI0NDMtYzgyemYzZjJvYWoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcxMzk1OSwiZXhwIjoxNzkyNzE0MjU5fQ.WHVOtB7mbmchVEy_6xQLO9qAA_SJFOqbL2ysCiFpVGk" width="400" class="aligncenter" /></figure>
<p>Sherry did some calculations and realized that:</p>
<p style="margin-left: 3rem">I. If she were to place the portions of money $A$, $B$ and $C$ into the savings accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$151.15$ at the end of a year.</p>
<p style="margin-left: 3rem">II. If she were to invest the portions of money $A$, $B$ and $C$ through the investment accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$426$ at the end of a year.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the exact amounts of the three portions of money $A$, $B$ and $C$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Sherry decides that she will place one of the portions of her money into the savings account of one bank and the remaining two portions into the investment accounts of the remaining two banks separately. Determine the maximum amount of money she can have after a period of one year.</span></div><p style="text-align: right;">[2]</p></li></ol>

Sherry has an initial sum of ${\$35 000}$ which she divided into three portions $A$, $B$ and $C$.

She is considering placing the portions of money into three separate banks that provide returns through savings account and investment account. The following table shows the returns on savings account and investment account provided by the three banks for a period of one year:

Sherry did some calculations and realized that:

I. If she were to place the portions of money $A$, $B$ and $C$ into the savings accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$151.15$ at the end of a year.

II. If she were to invest the portions of money $A$, $B$ and $C$ through the investment accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$426$ at the end of a year.

Find the exact amounts of the three portions of money $A$, $B$ and $C$.

Sherry decides that she will place one of the portions of her money into the savings account of one bank and the remaining two portions into the investment accounts of the remaining two banks separately. Determine the maximum amount of money she can have after a period of one year.

Math Question Bank