Question

(a) What is the future value of the following unequal cash flows using 9% interest rate?

YEAR                  1                2                3                   4                5

CASH FLOW   $600         $800           $500            $400           $900

(b) What would be an annuity payment (PMT) that would give the same future value

     using the same interest rate and same number of years?

(c) What is the present value of the following unequal cash flows using

      7.5% interest rate?

YEAR                  1                2                3                   4              

CASH FLOW   $950         $860           $520            $770          

(d) What would be the annuity payment (PMT) that would give the same present value

     using the same interest rate and same number of years?

Answer 1

Ans a ) Future value = 600 * (1.09)^4 + 800* (1.09)^3 + 500 * (1.09)^2 + 400 * (1.09)^1 + 900

= $3813

Ans b) Future value of annuity = payment * ((1+ r)^n - 1)/r

3813 = payment * (1.09^5 - 1)/.09

payment = 3813 * .09/.538624

Payment = 637.12

Ans c) Present value = 950/(1.075) + 860/(1.075)^2 + 520/(1.075)^3 + 770/(1.075)^4

= 883.72 + 744.19 + 418.58 + 576.58

= 2623

Ans d) Present value of annuity = payment * (1 - (1/(1+r)^n)/r

2623 = payment * (1 - (1/1.075)^4).075

Payment = 783.14