A perpetuity pays $280 per year and interest rates are 6.7 percent. How much would its value change if interest rates increased to 8.2 percent? (Round your answer to 2 decimal places.)

Answer: value decreases by $764.47

Explanation:

Given the following;

Coupon value (C) = $280, Thus is the interest amount paid annually.

Rate 1 (r1) = 6.7%

Rate 2 (r2) = 8.2%

Calculating the present value (PV) using;

PV = Coupon value : rate

At rate of 6.7%

PV = 280 : (6.7:100)

PV = 280 : 0.067 = $4179.10

At rate of 8.2%,

PV = Coupon value : rate

PV = 280 : (8.2:100)

PV = 280 : 0.082

PV = $3414.63

Difference in Present value of the two rates is given by;

$4179.10 - $3414.63 = $764.47

The value decreases in $764.47

Explanation:

Giving the following information:

Perpetuity pays $280 per year and interest rates are 6.7 percent.

New rate = 8.2 percent

First, we need to find the present value of the perpetual annuity at 6.7% interest rate:

PV = Cf/i

Cash flow = 280

i = 0.067

PV = 280/0.067 = $4,179.1

Now, we can calculate the new present value:

PV = 280 / 0.082 = $3,414.63