Question

A back pay certificate is offered for sale on which the yearly payments are P996, partly principal and partly interest. There are 8 annual payments still due, the first of these due one year from now. How much should one pay for this note in order to get 5% interest, compounded annually, on the investment?

Answer 1

Hi,

Hope you are doing well!

Question:

Answer:

Present value of total cash flow = CF/(1+r)^n

= CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 +CF4/(1+r)^4 +CF5/(1+r)^5 + CF5/(1+r)^6 + CF5/(1+r)^7 +CF5/(1+r)^8

= 996/(1+5%)^1 + 996/(1+5%)^2 + 996/(1+5%)^3 + 996/(1+5%)^4 + 996/(1+5%)^5 + 996/(1+5%)^6  + 996/(1+5%)^7 + 996/(1+5%)^8

= 996/(1.05)^1 + 996/(1.05)^2 + 996/(1.05)^3 + 996/(1.05)^4 + 996/(1.05)^5 + 996/(1.05)^6  + 996/(1.05)^7 + 996/(1.05)^8

= 996/1.05 + 996/1.1025 + 996/1.1576 + 996/1.2155 + 996/1.2762 + 996/1.3400 + 996/1.4071 + 996/1.4774

= 948.57 + 903.40 + 860.40 + 819.41 + 780.44 + 720.89 + 707.83 + 674.15 = 6416

Present value of total cash flow = 6416

How much should one pay for this note in order to get 5% interest, compounded annually, on the investment = 6416

Thank You