2 What is the present value of the following yearly receipts

2. What is the present value of the following yearly receipts? $2,250 annually for 20 years at 56 compounded annually, what is it for 9%? 3, what equal annual payment is necessary to repay $20,000 in 5 years at an interest rate of4.5% compounded annually? 4, Calculate the monthly payment for a 5 year $35,000 car loan at an interest rate of 6% compounded monthly.

Solution

(2)

(a) \"56 compounded annually\" - Interest rate is not clear.

(b) When interest rate is 9%,

Present value ($) = 2,250 x PVIFA(9%, 20) = 2,250 x 9.1285* = 20,539.13

(3)

Required payment ($) = 20,000 / FVIFA(4.5%, 5) = 20,000 / 5.4707** = 3,655.83

(4)

Monthly interest rate = 6%/12 = 0.5%

Number of months = 5 x 12 = 60

Monthly payment ($) = 35,000 / PVIFA(0.5%, 60) = 35,000 / 51.7256^# = 676.65

*From PVIFA Factor table

**FVIFA(r%, N) = [(1 + r)^N - 1] / r

FVIFA(4.5%, 5) = [(1.045)⁵ - 1] / 0.045 = (1.2462 - 1) / 0.045 = 0.2462 / 0.045 = 5.4707

#PVIFA(r%, N) = [1 - (1 + r)^-N] / r = [1 - (1.005)^-60] / 0.005 = (1 - 0.7414) / 0.005 = 0.2586 / 0.005 = 51.7256