Darryl plans to deposit $2,000 into a new account that offers an annual interest rate of 3.2%. He will make no additional deposits or withdrawals. Darryl can choose between an account at a bank and an account at a credit union:
• The bank compounds the interest annually.
• The credit union pays simple interest.
Which statement is true if Darryl leaves his money in the account for 4 years?
A. The bank will pay $12.55 more in interest in 4 years.
B. The accounts at the credit union and the bank will each earn $256 in interest in 4 years.
C. The credit union will pay $12.55 more in interest in 4 years.
D. The accounts at the credit union and the bank will each earn $268.55 in interest in 4 years.
A. The bank will pay $12.55 more in interest in 4 years.
Explanation:
For the bank account:
Principal = $2,000
Annual interest rate = 3.2%
Number of years = 4
Compounded annually
Using the formula for compound interest: A = P(1 + r/n)^(nt)
Where:
A = amount of money accumulated after n years, including interest
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case:
A = 2000(1 + 0.032/1)^(1*4)
A = 2000(1.032)^4
A = 2000(1.1311696)
A = $2,262.34
Interest earned = $2,262.34 - $2,000 = $262.34
For the credit union account:
Principal = $2,000
Annual interest rate = 3.2%
Number of years = 4
Simple interest
Using the formula for simple interest: I = P*r*t
Where:
I = interest earned
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
t = number of years
In this case:
I = 2000*0.032*4
I = $256
Therefore, the bank will pay $262.34 in interest and the credit union will pay $256 in interest, resulting in the bank paying $12.34 more in interest after 4 years.