Mini Case: 4 -31
or in part.
h. 2. Will the future value be larger or smaller if we compound an initial amount
more often than annually, for example, every 6 months, or semiannually, holding
the stated interest rate constant? Why?
h. 3. What is the future value of $100 after 5 years under 12% annual compounding?
Semiannual compounding? Quarterly compounding? Monthly compounding?
Daily compounding
Mini Case: 4 – 32
or in part.
h. 4. What is the effective annual rate (EAR or EFF%)? What is the EFF% for a
nominal rate of 12%, compounded semiannually? Compounded quarterly?
Compounded monthly? Compounded daily?
i. Will the effective annual rate ever be equal to the nominal (quoted) rate?
Mini Case: 4 -33
or in part.
j. 1. Construct an amortization schedule for a $1,000, 10% annual rate loan with 3
equal installments.
2. What is the annual interest expense for the borrower, and the annual interest
income for the lender, during Year 2?
Mini Case: 4 – 34
or in part.
k. Suppose on January 1 you deposit $100 in an account that pays a nominal, or
quoted, interest rate of 11.33463%, with interest added (compounded) daily.
How much will you have in your account on October 1, or 9 months later?
Answer: The daily periodic interest rate is IPER = 11.3346%/365 = 0.031054%. There are 273
days between January 1 and October 1. Calculate FV as follows:
FV273 = $100(1.00031054)273
= $108.85.
Mini Case: 4 -35
or in part.
Fractional time periods
Thus far all of our examples have dealt with full years. Now we are going to look at
the situation when we are dealing with fractional years, such as 9 months, or 10 years.
In these situations, proceed as follows:
As always, start by drawing a time line so you can visualize the situation.
Then think about the interest rate—the nominal rate, the compounding periods per
year, and the effective annual rate. If you have been given a nominal rate, you
may have to convert to the ear, using this formula:
EAR =
1
M
I
1
M
NOM
.
Mini Case: 4 – 36
or in part.
l. 1. What is the value at the end of Year 3 of the following cash flow stream if the
quoted interest rate is 10%, compounded semiannually?
0 1 2 3 Years
| | | | | | |
100 100 100
Answer: 0 1 2 3
| | | | | | |
Here we have a different situation. The payments occur annually, but compounding
5%