Question

On 10th January in each of the year 1964 to 1979 inclusive,an investor invested 500 pounds in a special bank savings account. On 10th January 1983 the investor withdrew his savings, given that the entire period the bank used an annual interest rate of 7% for his special savings account. Find the sum withdrawn by the investor

Answer 1

 We first find the accumulated value at the end of the 15 years(on 1979 10th January) of an annuity due as follows;

Accumulated value on 1979 10th January= $500\ddot{s}_{n\rceil}=500({(1+i)^{n}-1\over d})$

Where $n=15$ years , $i=0.07$ and $d={i\over 1+i}={0.07\over 1+0.07}={0.07\over 1.07}=0.06542056074766$

$500\ddot{s}_{n\rceil}=500({(1+i)^{n}-1\over d})$

$=500({(1+0.07)^{15}-1\over 0.06542056074766})$

$=500({(1.07)^{15}-1\over 0.06542056074766})$

$=13444.0267754679$ pounds

We then find the accumulated value at the end of the 4 years (On 10th January 1983) as follows;

accumulated value On 10th January 1983$=13444.0267754679(1+0.07)^4$

$=13444.0267754679(1.07)^4$

$=17622.3766556165$ pounds

$\therefore$ The investor widthdraw $17622.3766556165$ pounds