Question

You have deposited the other $400 in a savings account, which pays three percent interest compounded quarterly. Find the amount in the account for 0, 5, 10, 15, and 20 years, using the compound interest formula.

Fill in the table. Round the amounts to the nearest dollar.

Answer 1

Answer: Using the compound interest formula:

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

where:

A = the amount after t years

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

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

t = the number of years

For the savings account with $400 deposited and 3% interest compounded quarterly, we have:

n = 4 (compounded quarterly)

r = 0.03 (3% interest rate)

P = $400 (initial amount)

For 0 years, we have:

A = 400(1 + 0.03/4)^(4*0)

A = $400

For 5 years, we have:

A = 400(1 + 0.03/4)^(4*5)

A = $476

For 10 years, we have:

A = 400(1 + 0.03/4)^(4*10)

A = $567

For 15 years, we have:

A = 400(1 + 0.03/4)^(4*15)

A = $675

For 20 years, we have:

A = 400(1 + 0.03/4)^(4*20)

A = $804

So the completed table is:

Time (years) Amount in account

0 $400

5 $476

10 $567

15 $675

20 $804

Explanation: