Question

19. (Calculating the future value of an annuity) Find the future value of an annuity that pays €8,000 a year for 10 years at 6 percent compounded annually. What will be the future value if it was compounded at 10 percent?

Answer 1

If interest rate is 6%:

Annual Payment = 8,000
Number of Payments = 10
Interest Rate = 6%

Future Value = 8,000*1.06^9 + 8,000*1.06^8 + …. + 8,000*1.06 + 8,000
Future Value = 8,000 * (1.06^10 - 1) / 0.06
Future Value = 8,000 * 13.18079
Future Value = 105,446.32

If interest rate is 10%:

Annual Payment = 8,000
Number of Payments = 10
Interest Rate = 10%

Future Value = 8,000*1.10^9 + 8,000*1.10^8 + …. + 8,000*1.10 + 8,000
Future Value = 8,000 * (1.10^10 - 1) / 0.10
Future Value = 8,000 * 15.93742
Future Value = 127,499.36