Question

(Types of Interest HC)

A principal amount of $11,200 is placed in a savings account with an APR of 2.88% simple interest for 12 years. The same principal amount is placed in
a savings account with an APR of 3.19% compounded continuously for 9 years.
Part A: How much interest is earned in the simple interest account? Show all necessary steps. (3 points)
Part B: How much interest is earned in the continuously compounded interest account? Show all necessary steps. (3 points)
Part C: If the continuously compounded interest account was replaced with a monthly compounding account, what is the difference in the total account
balances for the two compounded interest accounts? Show all necessary steps. (4 points)

Answer 1

The simple interest earned on a principal amount of $11,200 with an APR of 2.88% for 12 years is $3,072. The interest earned in the continuously compounded interest account is $4,214.45. The difference in the total account balances for the two compounded interest accounts is -$3,000.8.

Step-by-step explanation:

Part A: To calculate the simple interest earned on a principal amount of $11,200 with an APR of 2.88% for 12 years, we can use the formula:

Simple Interest = Principal * Rate * Time

Simple Interest = $11,200 * 0.0288 * 12

Simple Interest = $3,072

Therefore, the interest earned in the simple interest account is $3,072.

Part B: To calculate the interest earned in the continuously compounded interest account, we can use the formula:

Compound Interest = Principal * e^(Rate * Time)

Compound Interest = $11,200 * e^(0.0319 * 9)

Compound Interest = $4,214.45

Therefore, the interest earned in the continuously compounded interest account is $4,214.45.

Part C: To calculate the difference in the total account balances for the two compounded interest accounts, we need to find the future value of each account. Using monthly compounding for the second account, we can use the formula:

Future Value = Principal * (1 + Rate/12)^(12 * Time)

Future Value for continuously compounded account = $11,200 * e^(0.0319 * 9)

Future Value for monthly compounding account = $11,200 * (1 + 0.0319/12)^(12 * 9)

Difference in account balances = Future Value for monthly compounding account - Future Value for continuously compounded account

Difference in account balances = $1213.65 - $4214.45

Difference in account balances = -$3,000.8

Therefore, the difference in the total account balances for the two compounded interest accounts is -$3,000.8.