2023 SJI P2 Q5

Bobby wants his savings to reach \(\$50\,000\) to help his daughter pay for her college education in \(5\) years’ time. He deposits \(\$25\,000\) into a savings account that gives an interest rate of \(5\%\) per annum compounded quarterly for \(5\) years. He does not deposit any more money or withdraw any money from the savings account during the \(5\) years.

1. By finding the amount of money Bobby has at the end of \(5\) years in the savings account, show that he will not be able to reach his target.[2]
2. Find the minimum amount, to the nearest dollar, that Bobby would need to deposit initially for him to reach his target.[2]

Other than depositing \(\$25\,000\) into the above savings account, Bobby plans to also deposit a fixed amount of money, \(\$p\), at the end of every month into another savings plan that gives an interest rate of \(2.6\%\) per annum, compounded half-yearly, for \(5\) years.

3. Find the minimum value of \(p\), to the nearest dollar, for Bobby’s savings to reach his target of \(\$50\,000\) at the end of \(5\) years.[3]