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

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

explanation: doctrine of respondeat superior is a legal doctrine that is commonly used in tort. this principle makes an employer or principal legally responsible for the wrongful acts done by an employee or agent, if such acts occur within the scope of the employment or agency.