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Marsha has an option between two savings accounts. Account #1 will only let her invest $4,500 but at 20% annual interest rate compounded quarterly, while Account #2 will let her invest $6,000 but only at a 15% annual interest rate compounded monthly. Which account option gives her the most interest if she only plans to invest her money for five years?

User Fikkatra
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1 Answer

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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.

User Thanuja
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