Question

How much will $8000 invested at 3 percent interest be worth in three years if it is compounded annually? Quarterly? How much if the interest rate is 5 percent?

Answer 1

At 3%:

Annual compounding:

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$8000(1.03)^3

=$8741.816

At 3% quarterly compounding:

We use the formula:
A=P(1+r/400)^4n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$8000(1+0.03/4)^(4*3)

=8750.46(Approx).

At 5%:

Annual compounding:

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$8000(1.05)^3

=$9261

At 5% quarterly compounding:

We use the formula:
A=P(1+r/400)^4n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$8000(1+0.05/4)^(4*3)

=9286.04(Approx).