Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.