A payment of 2000 will be realized today with additional pay

A payment of $2,000 will be realized today with additional payments of $1,000 at the end of each of the next 5 years. Assume a nominal interest rate of 20% is appropriate and calculate the following:

A) Determine the future value of all the payments at the end of five years from now.

B) What is the future value 5 years from now of the $2,000 plus $1,000 annual payments if the 20% nominal interest rate is compounded semi-annually?

C) What semi-annual payments are equivalent to the $1,000 payments each year if the 20% interest is compounded semi-annually?

Solution

(A)

Future value = $2,000 x (1.2)⁶ + $1,000 x FVIFA (20%, 5) = $2,000 x 2.986 + $1,000 x 7.4416

= $5,971.97 + $7,441.6 = $13,413.57

(B) For semi-annual compounding, relevant interest rate = 10% and number of periods = 5 x 2 = 10

FV = $2,000 x (1.1)¹⁰ + $1,000 x FVIFA (10%, 10)

= $2,000 x 2.5937 + $1,000 x 15.9374

= $5,187.48 + $15,937.4 = $21,124.88

(C)

With annual compounding, FV of $1,000 after 5 years = $1,000 x FVIFA (20%, 5) = $1,000 x 7.4416 = $7,441.6

If required semi-annual annuity be A, then

$7,441.6 = A x FVIFA (10%, 10) = A x 15.9374

A = $7,441.6 / 15.9374 = $466.93