Question

1. A 5-year annuity of $350 monthly payments begins in 10 years (the first payment is at the end of the first month of year 10, so it's an ordinary annuity). The appropriate discount rate is 12%, compounded monthly. What is the value of the annuity 4 years from today?

2.   A 5-year annuity of $350 monthly payments begins in 10 years (the first payment is at the end of the first month of year 10, so it's an ordinary annuity). The appropriate discount rate is 12%, compounded monthly. What is the value of the annuity today?

Answer 1

Assumption: Current time = t = 0, Monthly Annuity = $ 350, Annuity Duration = 5years or (5 x 12) = 60 months, Discount Rate = 12 % compounded monthly, Applicable Monthly Rate = 12/12 = 1 %, Annuity Begins at the end of the first month of Year 10 i.e one month after the end of Year 9.

Annuity Value at the end of Year 9 = 350 x (1/0.01) x [1-{1/(1.01)^(60)}] = $ 15734.3

Annuity Value at the end of Year 4 = 15734.3 / (1.01)^[12 x (9-4)] = $ 8660.92

NOTE: Please raise a separate query for the solution to the second unrelated question as one query is restricted to the solution of only one complete question with up to four sub-parts.