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Jonathan has a debt of $3,000 that needs to be repaid with 3 annual equal principal repayments with interest on the outstanding balance. The debt has an annual effective interest rate of 8%. In order to match his payment obligations exactly, Jonathan decides to purchase the following zero coupon bonds. Time to Maturity Par Value 1 year $1,000 2 years $ 800 3 years $ 900 Calculate the number of units of the 3-year bond Jonathan should buy, assuming fractional purchase is possible

Sagot :

Anthougoidn

Answer:

Jonathan

The number of units of the 3-year bond that Jonathan should buy is:

3.88 or 3 and 22/25 bonds.

Explanation:

a) Data and Calculations:

Present value of debt = $3,000

Annual effective interest rate = 8%

Total future value of the debt with interest = $3,492.30

Equal annual repayment of the debt = $1,164.10 ($3,492.30/3)

Number of 3-year bond that Jonathan should buy = $3,492.30/$900 = 3.88 or 3 and 22/25 bonds

Time to Maturity    Par Value

1 year                        $1,000

2 years                      $ 800

3 years                      $ 900

From an online calculator, the total amount to be paid with interest is $3,492.30:

N (# of periods)  3

I/Y (Interest per year)  8

PV (Present Value)  3000

FV (Future Value)  0  

Results

PMT = $1,164.10

Sum of all periodic payments $3,492.30

Total Interest $492.30

Answer:

1.2

Explanation:

Given that we are making 3 Equal Principle Payments on a loan of $3000, the principle that we will repay each year will be [tex]\frac{3000}{3} = $1000[/tex].

First Year:

The interest that we will need to repay during the first year will be 3000*.08 which will be $240 dollars of interest, so we will be paying a total of 1000 + 240, or $1240 for the first year reducing the amount due to $2000.

Second Year:

The interest that we will need to repay during the second year will be 2000*.08 which will be $160 of interest, so we will be paying a total of 1000 + 160, or $1160 which will reduce the amount due $1000.

Third Year:

This is the year that we care for. We have a total interest amount of $80, so we will be paying a total of $1080 for the third year.

Given that the par value of the Zero Coupon bond for the third year is $900, we will need [tex]\frac{1080}{900} = 1.2[/tex] coupons for the final year, giving us our answer of 1.2 3-year bonds that Jonathan should buy.

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