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Math

QuestionWhat price should Suresafe expect to sell a \$1,000 bond with 10% interest and 3 years to maturity if the return is 14%?

Studdy Solution

STEP 1

Assumptions1. The face value of the bond is $1,000. The bond has a nominal annual interest rate of10%
3. The bond has3 years to maturity4. Interest is payable annually5. The bond is held byuresafe Fire Insurance Company6.uresafe wishes to sell the bond7. The bond should provide a return of14% in current market conditions

STEP 2

First, we need to calculate the annual interest payment on the bond. This can be done by multiplying the face value of the bond by the interest rate.
Annual Interest Payment=Face ValuetimesInterest RateAnnual\, Interest\, Payment = Face\, Value \\times Interest\, Rate

STEP 3

Now, plug in the given values for the face value and interest rate to calculate the annual interest payment.
Annual Interest Payment=$1,000times10%Annual\, Interest\, Payment = \$1,000 \\times10\%

STEP 4

Convert the percentage to a decimal value.
10%=0.110\% =0.1Annual Interest Payment=$1,000times0.1Annual\, Interest\, Payment = \$1,000 \\times0.1

STEP 5

Calculate the annual interest payment.
Annual Interest Payment=$1,000times0.1=$100Annual\, Interest\, Payment = \$1,000 \\times0.1 = \$100

STEP 6

To find the price per bond thaturesafe should be able to realize on the sale, we need to calculate the present value of the bond. This is done by discounting the annual interest payments and the face value of the bond at the market interest rate (14%).
Price per bond=∑t=13Annual Interest Payment(1+Market Interest Rate)t+Face Value(1+Market Interest Rate)3Price\, per\, bond = \sum_{t=1}^{3} \frac{Annual\, Interest\, Payment}{(1 + Market\, Interest\, Rate)^t} + \frac{Face\, Value}{(1 + Market\, Interest\, Rate)^3}

STEP 7

Convert the market interest rate to a decimal value.
14%=0.1414\% =0.14

STEP 8

Now, plug in the given values for the annual interest payment, face value, and market interest rate to calculate the price per bond.
Price per bond=∑t=13$100(1+0.14)t+$1,000(1+0.14)3Price\, per\, bond = \sum_{t=1}^{3} \frac{\$100}{(1 +0.14)^t} + \frac{\$1,000}{(1 +0.14)^3}

STEP 9

Calculate the price per bond.
Price\, per\, bond = \frac{\$100}{( +.14)^} + \frac{\$100}{( +.14)^2} + \frac{\$100}{( +.14)^3} + \frac{\$,000}{( +.14)^3}Price per bond=$87.72+$76.94+$67.44+$752.32Price\, per\, bond = \$87.72 + \$76.94 + \$67.44 + \$752.32Price per bond=$984.42Price\, per\, bond = \$984.42uresafe should be able to realize a price of $984.42 per bond on the sale.

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