Calculate the present value of a perpetuity that will pay out $7,500 every six months. The first payment will be made four years from now. The interest rate earned is 8.6% compounded semi-annually.

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Quizplus · Accepted Answer

The present value of a perpetuity can be calculated using the formula PV = PMT / i, where PMT is the payment amount and i is the interest rate per period. Here, PMT = $7,500 and the semi-annual interest rate i = 8.6% / 2 = 4.3% or 0.043 as a decimal. Thus, PV = $7,500 / 0.043 = $174,418.60. However, this is the value at the beginning of the perpetuity, which starts 4 years from now. To find the present value today, we discount it back 8 periods (since payments are semi-annual and the first payment is 4 years away): PV = $174,418.60 / (1 + 0.043)^8 = $129,898 (approximately).

Calculate the Present Value of a Perpetuity That Will Pay