Question

g) What is the present value of an ordinary annuity of $1,000 per year for 7 years discounted back to the present at 10 percent? What would be the present value if it were an annuity due?

h) What is the future value of an ordinary annuity of $1,000 per year for 7 years compounded at 10 percent? What would be the future value if it were an annuity due?

i) You have just borrowed $100,000, and you agree to pay it back over the next 25 years in 25 equal end-of-year payments plus 10 percent compound interest on the unpaid balance. What will be the size of these payments?

j) What is the present value of a $1,000 perpetuity discounted back to the present at 8 percent?

k) Muffin Megabucks is considering two different savings plans. The first plan would have her deposit $500 every six months, and she would receive interest at a 7 percent annual rate, compounded semiannually. Under the second plan she would deposit $1,000 every year with a rate of interest of 7.5 percent, compounded annually. The initial deposit with Plan 1 would be made six months from now and, with Plan 2, one year hence.

(a) What is the future (terminal) value of the first plan at the end of 10 years?

(b) What is the future (terminal) value of the second plan at the end of 10 years?

(c) Which plan should Muffin use, assuming that her only concern is with the value of her savings at the end of 10 years?

(d) Would your answer change if the rate of interest on the second plan were 7 percent?

Answer 1

(g) Ordinary Annuity:

Annuity = $ 1000, Tenure = 7 years, Discount Rate = 10 %

Present Value (PV) = 1000 x (1/0.1) x [1-{1/(1.1)^(7)}] = $ 4868.42

Annuity Due:

Annuity = $ 1000, Tenure = 7 years, Discount Rate = 10 %

Present Value (PV) = 1000 x (1/0.1) x [1-{1/(1.1)^(7)}] x (1.1) = $ 5355.26

(h) Ordinary Annuity:

Annuity = $ 1000, Tenure = 7 years, Discount Rate = 10 %

Future Value (PV) = 1000 x (1.1)^(6) + 1000 x (1.1)^(5) + 1000 x (1.1)^(4) + .................+ 1000 = [{(1.1)^(7) - 1} / {1.1 - 1}] x 1000 = $ 9487.17

Annuity Due:

Annuity = $ 1000, Tenure = 7 years, Discount Rate = 10 %

Future Value (FV) = 1000 x (1.1)^(7) + 1000 x (1.1)^(6) +...........+ 1000 x (1.1) = [{(1.1)^(7) - 1} / {1.1 - 1}] x 1000 x (1.1) = $ 10435.89

(i) Borrowing = $ 100000. Tenure = 25 years and Interest Rate = 10 %

Let the equal annual repayments be $ P

100000 = P x (1/0.1) x [1-{1/(1.1)^(25)}]

P = 100000 / 9.07704 = $ 11016.81

(j) Perpetuity = $ 1000 and Discount Rate = 8 %

PV of Perpetuity = 1000 / 0.08 = $ 12500

NOTE: Please raise separate queries for solutions to the remaining sub-parts, as one query is restricted to the solution of only one complete question and/or four sub-parts.