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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.)

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facundobuzzetti

Answer:

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

fichoh

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

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