Question

Adam borrows an amount at an annual interest rate of 7%. He
repays all interest and principal in a lump sum at the end of ten
years from now. Adam uses the amount borrowed to purchase a 5-year
bond with a par value of 1, 000 with coupons at a nominal rate of
10% payable semiannually, with the first coupon paid at the end of
6-month period from now. The bond is redeemed at par and Adam’s
yield rate for the bond is 9% convertible semi- annually.

As Adam receives each coupon payment, he immediately puts the
money into an account earning nominal rate of 5.8% convertible
semiannually.

At the end of five years (from now), immediately after Adam
receives the final coupon payment, Adam deposits the accumulated
value of the coupons and the redemption amount of the bond into a
savings account earning an annual interest rate of 6%. At the end
of each year from year 6 through 10, Adam deposits an additional
amount of 50 into this savings account.

Find Adam’s accumulated value at the end of ten years after
the loan is re- paid.

Answer #1

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 20 years. She uses the amount borrowed to purchase a
10,000 par value 20-year bond with 8% semiannual coupons bought to
yield 6% convertible semiannually. All coupon payments are
reinvested at a nominal rate of 6% convertible semiannually.
Calculate the net gain to the investor at the end of 20 years after...

You pay $10,200 for a 12-year bond with a face value of $11,000
and semiannual coupons at a nominal annual rate of 6% convertible
semiannually. The bond can be called at face value on any coupon
date starting at the end of year 6. What is the minimum yield that
you could receive, expressed as a nominal annual rate of interest
convertible semiannually?

Eric deposits 100 into a savings account at time 0, which pays
interest at an annual nominal rate of i, compounded semiannually.
Mike deposits 200 into a different savings account at time 0, which
pays simple interest at an annual rate of i. Eric and Mike earn the
same amount of interest during the last 6 months of the 8th
year.

a) A seven-year $1000 bond has a nominal rate of 8% per annum,
with semiannual coupons, redeemable at par. The current market rate
is 6% compounded semiannually. Find the price of the bond.
b) A ten-year callable bond with par value 1000 and annual
coupons of 6%, has redemption value 1050 after 10 years and is
callable for 1050 after coupons are paid at end of years 6,7,8,9.
The purchase price is 1025. At the end of which year (6,7,8,9,10)...

A bond has a face amount of 1,000 and a term of n years. It is
bought to yield a nominal rate of 7% convertible semi-annually. The
bond will be redeemed for 1,100 at maturity. It pays semi-annual
coupons at 6% annual coupon rate. The present value of the coupon
is 426.50. What is the price of the bond?

Consider the following data:
Account A earns 8% nominal quarterly interest.
Account B earns 6% convertible interest twice a year.
At the end of 5 years the amount in account A is twice the amount
in account B.
At the end of 10 years the sum of the accumulated amount in both
accounts is $ 1,000
Analytically compute the sum of the accumulated amount
in both accounts at the end of 2 years.

1. A First State Bank savings account pays interest
semi-annually with an effective annual rate of 4.4%. What is the
stated or nominal interest rate the bank is offering?
2. An 8-year semi-annual payment coupon bond, $1,000 face, has
an expected return of 4% and a coupon of 6%. What is the bond’s
current yield?
3. You purchase a 4-year, 4% coupon bond for par. Interest is
paid annually. One year later, you sell the bond for $1,100. What
is your...

Allen deposits $100 into a fund today and $200 at the end of 30
years. Interest is credited at a quarterly nominal discount rate 6%
for the first 10 years, at a semiannually nominal interest rate of
8% for the next 10 years, and at a force of interest of 10%
thereafter. Calculate the accumulated value at the end of 40
years.

You purchased a $1,000 par value 20-year 4% coupon bond
with semi-annual payments for $1,000. Immediately after the
purchase, interest rates increased and the yield to maturity and
coupon reinvestment rate increased to 6%. (the coupons themselves
stayed at 4%) Interest rates and the yield to maturity remain at 6%
and you sell the bond 5 years later, having reinvested the coupons
at 6%. How much is in your account (proceeds from bond sale and
value of all coupons after...

A $1000 par value 6% bond with semiannual coupons matures at the
end of ten years. The bond is callable at $1100 five years after
issue. Find the maximum price that an investor can pay and still be
certain of a yield rate of (1) 5%, (2) 7%, convertible
semiannually. (Answers: (1) $1121.88, (2) $979.19). Show all work
and numerical equations please.

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