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An investor borrows an amount at an annual effective interest rate of 5% and will repay all interest and principal in a lump sum at the end of 10 years. She uses the amount borrowed to purchase a 1000 par value 10-year bond with 8% semiannual coupons bought to yield 6% convertible semiannually. All coupon payments are reinvested at a nominal rate of 4% convertible semiannually. Calculate the net gain to the investor at the end of 10 years after the loan is repaid.
a. 116
b.106
c. 111
d. 101

Sagot :

jepessoa

Answer:

d. 101

Explanation:

first we must determine the amount of the loan:

PV of face value = $1,000 / (1 + 3%)²⁰ = $553.68

PV of coupon payments = $40 x 14.877 (PV annuity factor, 3%, 20 periods) = $595.08

Loan amount = $1,148.76

Future value of the loan = $1,148.76 x (1 + 5%)¹⁰ = $1,871.21

You will receive 20 coupon payments of $40 each, which will be reinvested at 2% semiannual rate. You will also receive $1,000 corresponding to the face value of the bond.

Future value of the coupon payments = $40 x 24.297 (FV annuity factor, 2%, 20 periods)] = $971.88

Total money received at the end of the 10 year period = $971.88 + $1,000 = $1,971.88

Gain = $1,971.88 - $1,871.21 = $100.67 ≈ $101

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