Question

Last month Jim purchased $10,000 of U.S. Treasury bonds (their face value was $10,000). These bonds have a 30-year maturity period, and they pay 1.5%interest every threemonths (i.e., theAPRis 6%, and Jim receives a check for $150 every three months). But interest rates for similar securities have since risen to a 7% APR because of interest rate increases by the Federal Reserve Board. In view of the interest-rate increase to 7%, what is the current value of Jim’s bonds?

Answer 1

Answer:

current value is $8749.57

Explanation:

given data

face value = $10,000

maturity period = 30 = 30 × 4 = 120

interest = 1.5% every 3 month

solution

we will apply here bond price formula that is

bond price = coupon × $\frac{1 - (\frac{1}{(1+r)^n})}{r} + \frac{face value}{(1+r)^n}$          ............................1

here r is rate and n is no of period and

so rate = $\frac{7}{4}$ = 1.75% = 0.0175

and  coupon is $150

put here value

bond price = $150 × $\frac{1 - (\frac{1}{(1+0.0175)^{120}})}{0.0175} + \frac{10000}{(1+0.0175)^{120}}$  

bond price = 8749.57

so current value is $8749.57

Answer 2

The current value of Jim's bonds are $8,749.57.

What is the value of Jim's bonds?

The value of the bond can be determined by calculating the present value of the cash flows of the bonds. The present value is the sum of discounted cash flows.

Value of the bond = present value of coupon payments + present value of the face value of the bond at maturity.

Present value of the face value of the bond at maturity = $10,000 / (1 + 0.0175^120) = $1247.01

Present value of coupon payments = future value / (1 + 0.07^30)

Future value = amount x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

• Amount = 1.5% x 10,000 = $150
• r = interest rate = 7%/4

n = number of years = 30 x 4 = 120

$150 x [({1.0175^120) - 1} / 0.0175]  = $60,164.43

Present value = $60,164.43 / (1.0175^120) = $7,502.56

Value of the bond = $7,502.56 + $1247.01 =$8,749.57

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