Question

A 7-year annuity has annual payments of $2,500. The first payment is at the end of year 1. If interest is 5 percent per annum (effective annual rate) for 2 years followed by 6 percent per annum (effective annual rate) for 5 years, what is the future value of this annuity at the end of 7 years?

Please don't answer using excel.

Answer 1

Annual payment = $2,500
Number of payments = 7
Interest rate for first 2 years = 5%
Interest rate for next 5 years = 6%

Value of annuity at the end of 2 years = $2,500*1.05 + $2,500
Value of annuity at the end of 2 years = $2,625 + $2,500
Value of annuity at the end of 2 years = $5,125

Value of annuity at the end of 7 years = $5,125*1.06^5 + $2,500*1.06^4 + $2,500*1.06^3 + $2,500*1.06^2 + $2,500*1.06 + $2,500
Value of annuity at the end of 7 years = $5,125*1.06^5 + $2,500*(1.06^5 - 1)/0.06
Value of annuity at the end of 7 years = $5,125*1.338226 + $2,500*5.637093
Value of annuity at the end of 7 years = $20,951.14