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<p>Mei Lin deposits $ \$5000$ in an account that pays compound interest at $2\%$ per year.</p>
<ol class="abc-list"><li data-list-item-id="m02-q002-parts-1" data-list-item-path="m02-q002-parts-1"><div class="list-item-paragraph">Calculate the amount in the account after $4$ years.<span class="inline-marks">[4]</span></div></li><li data-list-item-id="m02-q002-parts-2" data-list-item-path="m02-q002-parts-2"><div class="list-item-paragraph">Hence, calculate the total interest earned.<span class="inline-marks">[4]</span></div></li></ol>

Mei Lin deposits $ \$5000$ in an account that pays compound interest at $2\%$ per year.

Calculate the amount in the account after $4$ years.

Hence, calculate the total interest earned.

Compound Interest

Sec 3/4 E Math Mock 2-Q02 - Mock Paper 2: Calculating compound interest

Standard Form and Compound Interest

<p>A sample contains $2.8\times10^{18}$ identical particles. The mass of each particle is $4.1\times10^{-22}$ grams. Calculate the total mass of the particles, giving your answer in standard form.<span class="inline-marks">[2]</span></p>

A sample contains $2.8\times10^{18}$ identical particles. The mass of each particle is $4.1\times10^{-22}$ grams. Calculate the total mass of the particles, giving your answer in standard form.

Standard Form

Sec 3/4 E Math Mock 1-Q04 - Mock Paper 1: Applying standard form to a scientific quantity

<p>Mei Lin deposits $ \$3000$ in an account that pays compound interest at $2\%$ per year.</p>
<ol class="abc-list"><li data-list-item-id="t03-q043-parts-1" data-list-item-path="t03-q043-parts-1"><div class="list-item-paragraph">Calculate the amount in the account after $4$ years.</div></li><li data-list-item-id="t03-q043-parts-2" data-list-item-path="t03-q043-parts-2"><div class="list-item-paragraph">Hence, calculate the total interest earned.</div></li></ol>

Mei Lin deposits $ \$3000$ in an account that pays compound interest at $2\%$ per year.

Sec 3/4 E Math T03-Q43 - Calculating compound interest

<p>A machine is bought for&nbsp;$\$45000$. Its value depreciates by $14\%$ each year. Calculate its value after $7$ years, giving your answer to the nearest dollar.</p>

A machine is bought for $\$45000$. Its value depreciates by $14\%$ each year. Calculate its value after $7$ years, giving your answer to the nearest dollar.

Sec 3/4 E Math T03-Q07 - Applying repeated percentage depreciation

<p>Gerald has $\$20 \; 000$ to invest in Company $\mathrm{A}$ or Company $\mathrm{B}$.</p>
<p>Company $\mathrm{A}$ offers $3.8\%$ per annum simple interest.</p>
<p>Company $\mathrm{B}$ offers $3.5\%$ per annum compound interest compounded half-yearly.  Gerald would like to invest this amount of money for a period of $5$ years.</p>
<p>Which company should he invest in? Explain your answer.</p>

Gerald has $\$20 \; 000$ to invest in Company $\mathrm{A}$ or Company $\mathrm{B}$.

Company $\mathrm{A}$ offers $3.8\%$ per annum simple interest.

Company $\mathrm{B}$ offers $3.5\%$ per annum compound interest compounded half-yearly.  Gerald would like to invest this amount of money for a period of $5$ years.

Which company should he invest in? Explain your answer.

Simple vs Compound Interest: Best Investment Choice

<p>Faith deposited $\$12 \; 000$ in Bank $\mathrm{A}$ that pays $2\%$ per annum simple interest.  </p>
<p>She also deposited the same amount in Bank $\mathrm{B}$ that pays $1.95\%$ per annum compound interest compounded monthly.  </p>
<p>Find the total amount of money she will receive from the two banks at the end of $3$ years.</p>

Faith deposited $\$12 \; 000$ in Bank $\mathrm{A}$ that pays $2\%$ per annum simple interest.  

She also deposited the same amount in Bank $\mathrm{B}$ that pays $1.95\%$ per annum compound interest compounded monthly.  

Find the total amount of money she will receive from the two banks at the end of $3$ years.

Total Returns from Two Banks: Simple vs Compound Interest

<p>Eddy borrowed a sum of money at a compound interest of $5\%$ per annum.</p>
<p>After $3$ years, he owed a total amount of $\$2315.25.$</p>
<p>Calculate how much he borrowed. </p>

Eddy borrowed a sum of money at a compound interest of $5\%$ per annum.

After $3$ years, he owed a total amount of $\$2315.25.$

Finding the Loan Principal from Compound Interest and Final Amount

<p>A sum of $\$25000$ was loaned from a bank that charges $r\%$ interest per year, compounded yearly.  </p>
<p>If after $3$ years, an amount of $\$28121.60$ was paid up to settle the loan, calculate $r$.</p>

A sum of $\$25000$ was loaned from a bank that charges $r\%$ interest per year, compounded yearly.  

If after $3$ years, an amount of $\$28121.60$ was paid up to settle the loan, calculate $r$.

Finding the Interest Rate from a Compound Interest Loan

<p>Darius invested some money in a savings account for&nbsp;$2$years.</p>
<p>The rate of compound interest was fixed at $10\%$ per annum compounded half-yearly.</p>
<p>At the end of the $2$ years there was $\$9724.05$ in his account.</p>
<p>How much did he invest in the account?</p>

Darius invested some money in a savings account for $2$years.

The rate of compound interest was fixed at $10\%$ per annum compounded half-yearly.

At the end of the $2$ years there was $\$9724.05$ in his account.

Finding the Principal from Compound Interest (Half-Yearly)

<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

Comparing Simple and Compound Interest Across Three Banks

<p>Betty invested $\$13 \; 000$ in an investment scheme that paid $4\%$ compound interest per annum.  </p>
<p>The investment is compounded half-yearly.  </p>
<p>Calculate the value of the investment after three years.</p>

Betty invested $\$13 \; 000$ in an investment scheme that paid $4\%$ compound interest per annum.  

The investment is compounded half-yearly.  

Calculate the value of the investment after three years.

Compound Interest with Half-Yearly Compounding Over 3 Years

<p>Ariel invested $\$5000$ in an investment fund that pays a compounded interest rate of $2\%$ per annum.  </p>
<p>Find the amount of money in the fund after the end of $2$ years if this amount is compounded quarterly.</p>

Ariel invested $\$5000$ in an investment fund that pays a compounded interest rate of $2\%$ per annum.  

Find the amount of money in the fund after the end of $2$ years if this amount is compounded quarterly.

Compound Interest with Quarterly Compounding Over 2 Years

<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

<p>Sam invested a sum of money into a savings account at an interest rate $4\%$ per annum, compounded yearly.  <br></p>
<p>Find the sum of money he invested if there was $\$16\mathrm{}872.96$ in his account at the end of $3$ years.</p>

Sam invested a sum of money into a savings account at an interest rate $4\%$ per annum, compounded yearly.  


Find the sum of money he invested if there was $\$16\mathrm{}872.96$ in his account at the end of $3$ years.

Problem involving Compound Interest

<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

<p>John borrowed $\$8000$ from a bank which charges compound interest at a rate of $16\%$ per annum.</p>
<p>Calculate </p>
<ol class="i-list"><li><div class="list-item-paragraph">the total amount of money that he owed the bank at the end of $3$ years, </div></li><li><div class="list-item-paragraph">the interest that he paid to the bank at the end of $3$ years.</div></li></ol>

John borrowed $\$8000$ from a bank which charges compound interest at a rate of $16\%$ per annum.

<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>

Simple Interest

<p>The mass of one atom of nitrogen is $2.33\times {{10}^{-11}}$ picograms. ($1$ pico $={{10}^{-12}}$)</p>
<ol class="i-list"><li><div class="list-item-paragraph">Express this mass in grams, giving your answer in standard form.</div></li><li><div class="list-item-paragraph">A molecule of nitrogen dioxide ${\left(\mathrm{NO}_2\right)}$ contains one atom of nitrogen and two atoms of oxygen.
</div><div class="list-item-paragraph">Given that the mass of one atom of oxygen is $2.66\times {{10}^{-23}}$grams, find the mass of one molecule of nitrogen dioxide.
</div><div class="list-item-paragraph">Give your answer in grams in standard form. </div></li></ol>

The mass of one atom of nitrogen is $2.33\times {{10}^{-11}}$ picograms. ($1$ pico $={{10}^{-12}}$)

Standard Form in Atomic Mass Calculations

<ol class="i-list"><li><div class="list-item-paragraph">The mass of the Sun is $1.99\times {{10}^{27}}$ tonnes.
</div><div class="list-item-paragraph">Write this mass, in kilograms, giving your answer in standard form. ($1$ tonne $=1000$kg)</div></li><li><div class="list-item-paragraph">The radius of a micro-organism is $0.000\,054\,65$cm.
</div><div class="list-item-paragraph">Express $0.000\,054\,65$cm in standard form, giving your answer correct to $3$ significant figures.</div></li></ol>

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