Question

How much interest is earned on an investment of $12,000 at 2.9% compounded daily for eight years

Answer 1

$3,113,34

Explanation:

The formula for calculating compound interest is

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

Where

A=the future total value, i.e, the money you will have after t years.

P=the initial deposit.

r=the annual interest rate.

n=the number of times that interest is compounded per year.

t=the number of years the money is saved.

In our case

A is unknown and we will have to calculate it with the formula.

P=$12,000

r=2.9%=0.029

n=365 because the interest is compounded daily and there are 365 days in a year

t=8 years

Applying the formula we get

`A=12,000(1+(0.029)/(365))^(365*8)`

`A=12,000(1+(0.029)/(365))^(2,920)`

`A=12,000(1.000079)^(2,920)`

So A=15,113.336

This is the amount of money you would have after 8 years.

Subtracting the initial deposit from this amount we obtain the interest earned I

I=15,113.336-12,000=3,113.336

Rounded to the nearest hundreth

I=$3,113,30