Mr Tan set aside $\$80\,000$ for his two sons. On the first day of the year that his sons turned \

Question

Mr Tan set aside $\$80\,000$ for his two sons. On the first day of the year that his sons turned $7$ and $17$ years old, he deposited $\$x$ into the younger son’s bank account and the remaining sum of money into the elder son's bank account. Mr Tan adds a further $\$1000$ into the younger son’s account on the first day of each subsequent year. The bank pays a compound interest at a rate of $2\%$ per annum on the last day of each year. Each son will withdraw the full sum of money from his account (after interest had been added) on the last day of the year that he turns $21$ years old. Find the amount of money the elder son will withdraw in terms of $x$. Leave your answer in exact form.[1] Find the amount of money, in terms of $n$ and $x$, in the younger son’s bank account at the end of the $n$ th year, where $n\ge 2$.[3] Using answer from (ii), show if Mr Tan had initially deposited $\$20\,000$ into the younger son’s account, the younger son would withdraw $\$43,\,210.78$.[2] Find the value of $x$ if Mr Tan wanted both sons to receive the same withdrawal amount, giving your answer to the nearest integer.[2]

Accepted Answer

(b)(i) ${{1.02}^{5}}\left( 80000-x \right)$ (ii) ${{1.02}^{n}}x+51000\left( {{1.02}^{n-1}}-1 \right)$ (iv) $\$29402$ (nearest integer)

2015 TJC P2 Q2 [Modified]

2015 TJC P2 Q2 [Modified]

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