Question #299695

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that over the entire period the bank used an annual interest rate of 7% for its special savings accounts, find the sum withdrawn by the investor.

1
Expert's answer
2022-02-22T11:16:44-0500

Solution:

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

D=500(19791964+1)=50016=8000D=500(1979-1964+1)=500\cdot 16 =8000

The amount RR earned from the interest rate:

R=5000,07(19831964)+5000,07(19831965)++5000,07(19831979)=5000,0719+5000,0718++5000,074=5000,07(19+18++4)=5000,070,5(19+4)16=350,52316=6440R=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Finally find the sum SS withdrawn by the investor:

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

Answer: 14440

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