please give formula and how to solve this with answers. [10 points, 2 points eac

Question

please give formula and how to solve this with answers.

[10 points, 2 points each] An investor is considering the purchase of a 20-year7% coupon bond selling for $816 and a par value of $1,000. The yield to maturity for this bond is 9%. Answer the below questions. · What would be the total future dollars if this investor invested $816 for 20 years earning 9% compounded semiannually? What are the total coupon payments over the life of this bond? What would be the total future dollars from the coupon payments and the repayment of principal at the end of 20 years? For the bond to produce the same total future dollars as in part (a), how much must the interest on interest be? Calculate the interest on interest from the bond, assuming that the semiannual coupon payments can be reinvested at 4.5% every six months and demonstrate that the resulting amount is the same as in part (d

Explanation / Answer

(a) total future dollars if $ 816 invested at 9%, semi annually compunded

FV = PV (1 +i/k)nk

PV =$816, i =9%, k=2

FV = $816 (1 +0.09/2)20*2 = $816 (1.045)40 = $816(5.8164) = $ 4746.18

(b) TOTAL COUPON PAYMENT

COUPON RATE = 7%, FV =$1000

SO INTEREST = $1000 X 7% = $70/2 = $35 INTEREST WILL BE EVERY 6 MONTHS

TOTAL COUPONS WILL BE 20 YEARS X 2 PAYMENTS EVERY YEAR = 40 PAYMENTS

TOTAL COUPON PAYMENTS = $35 X 40 = $1400

(c) THE FUTURE VALUE OF COUPON PAYMENTS AND REPAYMENT OF PRINCIPAL

FUTURE VALUE OF COUPONS = FV ANNUITY = a/(i/k) [(1+i/k)n*k - 1]

i =9%, k =2

FV = $35/(0.09/2)* [(1 +0.09/2)20*2 - 1 ]= $35/0.045 *(1.045)40 = $777.78(5.8164 - 1) = $ 3746.10

PRINCIPAL IS PAID AT THE END OF 20 YEARS SO FV =$1000

SO TOTAL OF FUTURE VALUE OF COUPONS AND PRINCIPAL =$ 3746.10 + $1000 = $4746.10

(d)

THE INTEREST ON INTEREST WILL BE =

THE FUTURE VALUE OF ANNUITY OF INTEREST - TOTAL COUPON PAYMENTS

$ 3746.10 (ANSWER AS PER ABOVE c) - $1400 (ANSWER AS PER ABOVE b) = $2346.10

(e) 4.5% rate of reinvestment every six months

FUTURE VALUE OF ALL COUPON PAYMENTS = $35/0.045 *(1.045)40 = $777.78(5.8164 - 1) = $ 3746.10

COUPON PAYMENTS = $35*40 = $1400

SO THE DIFFERENCE OF AMOUNT = $3746.10 - $1400 = $2346.10 SAME AS ABOVE IN d

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.