A perpetuity pays $250 per year and interest rates are 5.5 percent. How much would its value change if interest increased to 8.5 percent? Did the value increase or decrease?

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Quizplus · Accepted Answer

The value of a perpetuity is calculated using the formula $ \text{Value} = \frac{PMT}{r} $, where PMT is the payment per period and r is the interest rate per period. Initially, the value is $ \frac{250}{0.055} = \$4,545.45 $. After the increase, the value is $ \frac{250}{0.085} = \$2,941.18 $. The change in value is $ \$4,545.45 - \$2,941.18 = \$1,604.27 $, and the value decreases because a higher discount rate reduces the present value of future payments.

A Perpetuity Pays $250 Per Year and Interest Rates Are