Answer to Question #299695 in Financial Math for Tony

Question

1. On 15 November in each of the years 1964 to 1979 inclusive an investor deposited £500 in a special bank savings account. On 15 November 1983 the investor withdrew his savings. Given that over the entire period the bank used an annual interest rate of 7% for its special savings accounts, find the sum withdrawn by the investor.

Answer 1

Solution:

The total sum $D$ deposited by an investor from 1964 to 1979 is:

$D=500(1979-1964+1)=500\cdot 16 =8000$

The amount $R$ earned from the interest rate:

$R=500\cdot 0,07\cdot (1983-1964)+500\cdot 0,07\cdot (1983-1965)+\cdots + 500\cdot 0,07\cdot (1983-1979)= 500\cdot 0,07\cdot 19+500\cdot 0,07\cdot 18+\cdots + 500\cdot 0,07\cdot 4= 500\cdot 0,07(19+18+\cdots + 4)=500\cdot 0,07\cdot 0,5(19+4)16=35\cdot 0,5\cdot 23\cdot 16 =6440$

Finally find the sum $S$ withdrawn by the investor:

$S=D+R=8000+6440=14440$

Answer: 14440