04 Jun WHAT IS THE NOMINAL RATE OF INTEREST COMPOUNDED SEMI-ANNUALLY?
1- To provide for expansion, a company has established a sinking fund earning 7% semiannually. The fund is anticipated to reach a balance of $72000 in fifteen years.
Payments are made at the beginning of every six months. What is the size of the semiannual payments?
2- A $25000, 9.5% bond with semi-annual coupons redeemable at par is bought sixteen
years before maturity at 78.25% of its face value. Calculate the approximate yield
rate.
3- A $50000, 7.2% bond with quarterly interest coupons redeemable at par in ten years is
purchased to yield 8% compounded quarterly. What is the purchase price of the bond?
(Example 15.2E on page 646).
4- A mortgage of $95000 is amortized over 25 years by monthly payments of $748.06.
What is the nominal rate of interest compounded semi-annually?
5- How long will it take to accumulate $18000 at 6% compounded monthly if $125 is
deposited in an account at the beginning of every month?
6- Robert deposited $100 in a trust account on the day of his sons birth and every three
months thereafter. If interest paid is 7% compounded quarterly, what will the balance
in the trust account be before the deposit is made on the sons twenty-first birthday?
7- The alumni of a college collected $32000 to provide a fund for ongoing bursaries. If
the money is invested at 7% compounded annually, what is the size of bursary that
can be paid every six months? (Example 13.5E on page 554).
8- What sum of money invested today at 8% compounded quarterly will provide for
payments of $2500 to be paid at the end of each year indefinitely? (Example 13.5C on
page 554).
9- What is the nominal rate of interest compounded monthly at which payments of $200
made at the end of every three months accumulate to $9200 in eight years?
10- What single cash payment is equivalent to payments of $3500 every six months at 7%
compounded quarterly if the payments are made at the end of every six months for
fifteen years?
11- How long will it take to build up a fund of $10,000 by saving $300 at the end of every
six months at 4.5% compounded semi-annually?
12- A contract is signed requiring payments of $750 at the end of every three months for
eight years. How much is the cash value of the contract if money is worth 10.5%
compounded quarterly?
13- A second mortgage requires payments of $370 at the end of each month for 15 years.
If interest is 11% compounded semi-annually, what was the amount borrowed? (Example
12.2B on page 481).
14- Payments of $500 deferred for nine years are received at the end of each month from
a fund of $10000 deposited at 10.5% compounded monthly. Determine the size of the
final payment. (Example 14.3D on page 605).
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