Question

cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 at the end of 3 years. what is the smallest amount, to the nearest pound she can invest

Answer 1

The smallest amount is
`\£6,911`

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1`

substitute in the formula above

`8,000=P(1+(0.05)/(1))^(1*3)`

solve for P

`8,000=P(1.05)^(3)`

`P=8,000/(1.05)^(3)`

`P=\£6,910.70`

Round to the nearest pound she can invest

The smallest amount is
`\£6,911`