Question

Read the example about how to calculate the present value of an ordinary annuity. Now consider a slightly different question. You loaned $57,134 to a firm just now. The term is 11 years. The firm promises to pay you an annual interest of $5,636 at the end of each year. Moreover, it will will also repay the principal on the due date. The annual discount rate is 6%. Please use a financial calculator to find the present value of all the payments that the firm will make to you regarding the loan. 

Hints: 

• The sequence of interest payments is an ordinary annuity, 

• The payment of the principal on the due date should be entered as FV. 

• All payments are cash inflows for you, so they should all be entered as positive numbers.

Answer 1

Annual interest received = $5,636

The principal amount ($57,134) will be re-paid at the end of the loan term. 

Discounting rate = 6%

 

Present value (PV) of inflows = PV of interests received (+) PV of the principal amount

                                                         = Present value annuity factor @ 6% for 11 years * annual interest (+) Present value factor @ 6% of 11th year

                                                         = 7.886 * $5,636 (+) 0.5267 * $57,134

                                                         = 44,450.42 + 30,092.47 

                                                         = $ 74,542.90

Present value (PV) of inflows = $ 74,542.90