Question

Cynthia invests some money in a bank which pays 5% compound interest per year she wants it to be over 8000 at the end of three years what is the smallest amount to the nearest pound she can invest

Answer 1

The smallest amount to the nearest pound she can invest is £6,911

Explanation:

Let

x -----> amount of money to be invested

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\\ P=x\\r=5\%=5\100=0.05\\n=1\\A>\£8,000`

substitute in the formula above

`x(1+(0.05)/(1))^(1*3)> 8,000`

`x(1.05)^(3)> 8,000`

`x> 8,000/(1.05)^(3)`

`x> \£6,910.70`

therefore

The smallest amount to the nearest pound she can invest is £6,911