Final answer:
Marsha earns more interest with Account #2, which has a higher initial investment and a slightly lower interest rate but with more frequent compounding. After calculating the future values, Account #2 yields $12,217.82 whereas Account #1 yields $11,847.29 over five years.
Step-by-step explanation:
To determine which savings account option gives Marsha the most interest after five years, we need to calculate the future value of investments in both accounts with their respective interest rates and compounding frequencies.
For Account #1, the future value with quarterly compounding is given by:
FV = P(1 + r/n)^(nt)
Where:
- P = $4,500 (initial investment)
- r = 0.20 (annual interest rate)
- n = 4 (times interest is compounded per year)
- t = 5 (number of years)
FV = 4500 (1 + 0.20/4(^(4*5)
Account #2, with monthly compounding, has the following future value:
FV = P(1 + r/n)^(nt)
Where:
- P = $6,000
- r = 0.15
- n = 12
- t = 5
FV = 6000 (1 + 0.15/12(^(12*5)
We then calculate the future value for both accounts:
Account #1: FV = 4500 (1.05(^(20) = $11,847.29
Account #2: FV = 6000 (1.0125(^(60) = $12,217.82
Marsha will earn more interest with Account #2 after five years.