Question

Given the Uniform Amount of an annual payment, A = $16,000 per year, an interest rate, i=9%, and a time period, n=6 years, calculate the unknown Present Worth of the amount borrowed, P=? Please show all work

Answer 1

Annual Payment = 16000$

Interest rate = 9 %

Time = 6 Years

Present worth = present value of payment in year1 + ..... upto Year 6

= 14678.89 + 13466.87 + 12354.93 + 11334.80 + 10398.90 + 9540.27

= 71774.66

1. Present value of payment in Year 1 = Future value / (1 + R)^n

= 16000 / (1 + 9%)^1

= 16000 / (1 + 0.09)^1

= 16000 / 1.09 = 14678.89 $

2.Present value of payment in Year 1 = Future value / (1 + R)^n

= 16000 / (1 + 9%)^2

= 16000 / (1.09)^2 = 16000 / 1.1881

= 13466.87 $

3.Present value of payment in Year 1 = Future value / (1 + R)^n

= 16000 / (1 + 9%)^3

= 12354.93 $

4.Present value of payment in Year 1 = Future value / (1 + R)^n

= 16000 / (1 + 9%)^4

= 11334.80 $

5.Present value of payment in Year 1 = Future value / (1 + R)^n

= 16000 / (1 + 9%)^5

= 16000 / 1.5386239549

= 10398.90 $

6.Present value of payment in Year 1 = Future value / (1 + R)^n

= 16000 / (1 + 9%)^6

= 9540.27 $