Suppose you put money into two different bank accounts. In Account #1 you deposit $500 and you will be earning 6% interest compounded quarterly. In Account #2 you deposit $600 and you will be earning 5% interest compounded annually. Which statement below best describes the relationship between the amount of money in Account #1 and Account #2 after 10 years have passed? Assume that during these years you do not withdraw any money.
(1 point)
Responses
Account #1 will have approximately $397 less than Account #2.
Account #1 will have approximately $397 less than Account #2.
Account #1 will have approximately $82 more than Account #2.
Account #1 will have approximately $82 more than Account #2.
Account #1 will have approximately $70 less than Account #2.
Account #1 will have approximately $70 less than Account #2.
Account #1 and Account #2 will have approximately the same amount of money in them.
To find the future value of the money in Account #1, we can use the formula for compound interest:
Future Value = Principal * (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Number of Years)
For Account #1:
Principal = $500
Interest Rate = 6% = 0.06
Number of Compounding Periods = 4 (quarterly compounding, so 4 times a year)
Number of Years = 10
Future Value in Account #1 = $500 * (1 + 0.06 / 4)^(4 * 10) = $500 * (1.015)^40 ≈ $819.43
For Account #2:
Principal = $600
Interest Rate = 5% = 0.05
Number of Compounding Periods = 1 (annual compounding)
Number of Years = 10
Future Value in Account #2 = $600 * (1 + 0.05 / 1)^(1 * 10) = $600 * (1.05)^10 ≈ $932.64
Therefore, Account #1 will have approximately $819.43 and Account #2 will have approximately $932.64 after 10 years have passed.
Account #1 will have approximately $113.21 less than Account #2.
None of the given statements accurately describes the relationship between the amount of money in Account #1 and Account #2 after 10 years have passed.