Question
What is the future value of an annuity with monthly payments of $100 over the course of five years with an APR of 4.5 percent?
Round the answer to the nearest hundredth. (1 point)
Round the answer to the nearest hundredth. (1 point)
Answers
Answered by
GPT 3.5
The future value of an annuity formula is:
FV = Pmt * [(1 - (1 + r)^-n) / r]
Where:
FV = future value of the annuity
Pmt = monthly payment amount ($100)
r = monthly interest rate (APR/12 = 0.045/12 = 0.00375)
n = total number of payments (5 years * 12 months = 60)
FV = $100 * [(1 - (1 + 0.00375)^-60) / 0.00375]
FV = $100 * [(1 - (1.00375)^-60) / 0.00375]
FV ≈ $100 * [(1 - 0.648453) / 0.00375]
FV ≈ $100 * [0.351547 / 0.00375]
FV ≈ $100 * 93.87867
FV ≈ $9,387.87
Therefore, the future value of an annuity with monthly payments of $100 over five years with an APR of 4.5 percent is approximately $9,387.87.
FV = Pmt * [(1 - (1 + r)^-n) / r]
Where:
FV = future value of the annuity
Pmt = monthly payment amount ($100)
r = monthly interest rate (APR/12 = 0.045/12 = 0.00375)
n = total number of payments (5 years * 12 months = 60)
FV = $100 * [(1 - (1 + 0.00375)^-60) / 0.00375]
FV = $100 * [(1 - (1.00375)^-60) / 0.00375]
FV ≈ $100 * [(1 - 0.648453) / 0.00375]
FV ≈ $100 * [0.351547 / 0.00375]
FV ≈ $100 * 93.87867
FV ≈ $9,387.87
Therefore, the future value of an annuity with monthly payments of $100 over five years with an APR of 4.5 percent is approximately $9,387.87.
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