One of your clients has asked your advice on the best way to accept payment on a

Question

One of your clients has asked your advice on the best way to accept payment on a sale. The client has been offered $220,000 immediately or $37,000 per year for ten years with the first payment due immediately. The appropriate interest rate is 10%. Present value factors for the present value of an ordinary annuity of $1 per period are shown below.





9 periods


10%


5.75902




10 periods


10%


6.14457




11 periods


10%


6.49506



The present value of the $37,000 annuity is:

1)$250,084
2)$240,317
3)$220,000

please show work

Explanation / Answer

The given problem is a model of Annuity due: To calculate the Annuity due, we need to find out the Present value of annuity. Calculating the present value of annuity using formula: Annuity present value = C * [(1 - Present value factor) / r] Where Present value factor = [1/(1+r)^t]                                           = [1 / (1 + 0.1)^10]                                           = [1 / 2.5937]                                           = 0.3855 Annuity present value = $37,000 * [(1 - 0.3855) / 0.1]                                  = $37,000 * 6.14457                                  = $227,350 Calculating the value of annuity due: Annutiy due = Annuity present value (1 + r)                    = $227,350 ( 1 + 0.1)                    = $250,084 Therefore, the present value of annuity due is $250,084 The correct option is 1) $250,084

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