Question

  Marian Kirk wishes to select the better of two 10-year annuities, C and D. Annuity C is an ordinary annuity of $2,500 per year for 10 years. Annuity D is an annuity due of $2,200 per year for 10 years.

1. Find the future value of both annuities at the end of year 10, assuming that

   Marian can earn (1) 10% annual interest and (2) 20% annual interest.

2. Use your findings in part a to indicate which annuity has the greater future

   value at the end of year 10 for both the (1) 10% and (2) 20% interest rates.

3. Find the present value of both annuities, assuming that Marian can earn (1)

   10% annual interest and (2) 20% annual interest.

4. Use your findings in part c to indicate which annuity has the greater present

   value for both (1) 10% and (2) 20% interest rates.

5. Briefly compare, contrast, and explain any differences between your findings

   using the 10% and 20% interest rates in parts b and d

Answer 1

Future value of ordinary annuity = P*[(1+r)^n - 1 / r ]

Future value of annuity due = P*[(1+r)^n - 1 / r]*(1+r)

Present value of ordinary annuity = P*[1 - (1+r)^-n / r ]

Present value of annuity due = P*[1 - (1+r)^-n / r ]*(1+r)

P = Annual payments

r = interest rate

n = number of periods

The main difference between ordinary annuity and annuity Due is in case of ordinary annuity payments will be made at the end of the year i.e., at the end of year 1 , end of year 2 e.t.c., How ever in case of annuity due Payments will be made at the beginning of the year i.e., at the beginning of year 1 , year 2 e.t.c.,

under both Present value and future value, when interest rate is 10%, Annuity C should be selected because it gives higher amounts and also gives higher annual payments (i.e., 2500)

how ever when interest rate is 20% eventhough Annuity C gives higher annual amounts (2500) it should not be selected because Annuity D has higher present and future values because of higher interest rate and beginning of payments

Formulas will be as follows: