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:%0D%0A%0D%0AThe bank compounds the interest annually.%0D%0AThe credit union pays simple interest.%0D%0AWhich 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 $256.55 in interest in 4 years
A. the bank will pay $12.55 more in interest in 4 years
Explanation:
For the bank account, with annual compounding, the formula to calculate the future value of the investment is:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value (initial deposit)
r = annual interest rate
n = number of years
Plugging in the values:
FV_bank = $2,000 * (1 + 0.032)^4
FV_bank = $2,000 * (1.032)^4
FV_bank = $2,000 * 1.1313
FV_bank = $2,262.64
Interest earned at the bank = $2,262.64 - $2,000 = $262.64
For the credit union account, with simple interest, the formula to calculate the future value of the investment is:
FV = PV * (1 + r * t)
Where:
FV = Future Value
PV = Present Value (initial deposit)
r = annual interest rate
t = time in years
Plugging in the values:
FV_credit_union = $2,000 * (1 + 0.032 * 4)
FV_credit_union = $2,000 * (1 + 0.128)
FV_credit_union = $2,000 * 1.128
FV_credit_union = $2,256
Interest earned at the credit union = $2,256 - $2,000 = $256
The difference in interest earned between the bank and the credit union in 4 years is $262.64 - $256 = $6.64, which is not $12.55 as stated in the options. Therefore, option A is not correct.