Peter Lynchpin wants to sell you an investment contract that pays equal $13,300

Question

Peter Lynchpin wants to sell you an investment contract that pays equal $13,300 amounts at the end of each of the next 23 years.

If you require an effective annual return of 8 percent on this investment, how much will you pay for the contract today? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Value today $

Peter Lynchpin wants to sell you an investment contract that pays equal $13,300 amounts at the end of each of the next 23 years.

Required:

Explanation / Answer

This is an ordinary annuity or a deferred annuity as the cash inflow of $13,300 is occuring at the end of each year.

We have to find the present value of this annuity.

Amount = $13,300. rate = 8%.

Present value = 13,300*(1/1.08)^1+13,300*(1/1.08)^2+13,300*(1/1.08)^3.....13,300*(1/1.08)^23

formula = amount*(1/1+annual rate)^time

Alternatively, we can use the PV factor of ordinary annuity for n = 23 years and r = 8%. From the annuity table, this factor is 10.3711. So, PV = annuity amount*PV factor = 13,300*10.3711 = 137,935.60.

Thus value today is $137,935.60

Year Amount 1+interest rate PV 1 13,300 1.08 12,314.81 2 13,300 11,402.61 3 13,300 10,557.97 4 13,300 9,775.90 5 13,300 9,051.76 6 13,300 8,381.26 7 13,300 7,760.42 8 13,300 7,185.58 9 13,300 6,653.31 10 13,300 6,160.47 11 13,300 5,704.14 12 13,300 5,281.61 13 13,300 4,890.38 14 13,300 4,528.13 15 13,300 4,192.71 16 13,300 3,882.14 17 13,300 3,594.58 18 13,300 3,328.31 19 13,300 3,081.77 20 13,300 2,853.49 21 13,300 2,642.12 22 13,300 2,446.41 23 13,300 2,265.19 Total 137,935.08

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