Question

Assume the prevailing interest rate is 5% per annum. A 4 -year lease agreement requires you to pay $1650 up front, followed by payments of $1650, $1650, and $1650 at the beginning of each of the following three years, respectively. What would the payment on a 4-year lease with a constant annual payment have to offer for you to be indifferent between the two lease options? Assume that the first payment on the constant annual payment lease will be made at the end of the first year, and round your answer to the nearest dollar.

A.

$1,650

B.

$1,650

C.

$1,733

D.

$1,678

Answer 1

PV of annuity for making pthly payment-Annuity Due
P = PMT+PMT x (((1-(1 + r) ^- (n-1))) / r)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
n = the number of periods in which payments will be made
PMT	1650
r	5%
n	4
PV=	1650+1650* (((1-(1 + 5%) ^- (4-1))) / 5%)
PV=	6,143.36
Keeping Same PV what should be annual payment
PV of Annuity paid in arrear
P = PMT x (((1-(1 + r) ^- n)) / r)
6143.36=	PMT x (((1-(1 + 5%) ^- 4)) / 5%)
6143.36=	PMT * 3.54595
PMT=	6143.36/3.54595
PMT=	1733
So correct answer is option C