Mr Chan plans to buy a new car in $2031$, which costs $\$120000$ in $2021$. There is a yearly

Question

Mr Chan plans to buy a new car in $2031$, which costs $\$120000$ in $2021$. There is a yearly inflation rate of $0.5\%$ on the price of the car. Show that the cost of the car in $2031$ with inflation is $\$126136.82$.[2] Mr Chan comes across a savings plan in a local bank that pays $1.5\%$ interest on $31$ December of each year. In order to buy the car on $31$ December $2031$, he intends to save $\$y$ every year starting from $1$ January $2022$ for $10$ years with this bank without any withdrawal. On $1$ January $2022$ Mr Chan puts $\$y$ into the bank, and on the $1$ January of each subsequent year, he puts another $\$y$ into the bank. Find the least value of $\$y$ correct to the nearest dollar.[5] Mr Chan's daughter, Elly, wants to buy a gift for her brother and works out a savings plan with her father. The plan is for $n$ months and Elly will save $\$5$ at the start of every month in a piggy bank. She saves her first $\$5$ on $1$ May $2021$. To help Elly, Mr Chan adds $\$5$ in the piggy bank on the last day of May. For the subsequent months, he puts in $\$5$ more than the previous month in the piggy bank on the last day of each month, so that he puts in $\$5$ in May, $\$10$ in June, and so on. If the gift costs $\$120$, write down an inequality involving $n$ and solve it. Find the date when Elly will save enough money in her piggy bank to buy the gift.[5]

Accepted Answer

(i) $126136.82\text{ dollars}$ (ii) $11612\text{ dollars}$ (iii) $n=6$, 31 October 2021

2021 JPJC J2 MYE P1 Q10

2021 JPJC J2 MYE P1 Q10

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