G. Additional Exercises
- In all of the problems we have looked at so far, we have assumed that the interest rate remains constant. For some situations
(such as most CDs) this is a reasonable assumption. However, in many other situations the interest rate may well change.
Suppose that Sandra deposits $1,350 in a bank account for 5 years. For the fi rst 2 years, the account pays 6%
compounded monthly, then for the last 3 years the account pays 5.4% compounded quarterly.
a. Find the value of Sandra’s account at the end of the fi rst 2 years.
b. Find the value of Sandra’s account at the end of the next 3 years. (Hint: Your answer to (a) will be the PV for the
last 3 years.)- In Example 3.2.9 we said that using a 365-day year and 30 days per month will usually, but not always, underestimate
the number of days. Give an example where this rule does not underestimate the number of days. - On April 3, 2006, I deposited $4,302.59 in a certifi cate of deposit paying 5.73% compounded daily. The certifi cate
matured on July 9, 2007. What was the maturity value? - Repeat Exercise 38 from Section 3.1, this time assuming that the interest is compounded daily. Does daily compounding
affect your assessment of Rule of 70 versus Rule of 72? - Find the amount of interest earned on a $3,000 investment at 5.5% for 3 years, assuming interest compounds every
nanosecond.
3.3 Effective Interest Rates
Comparing Interest Rates
Whether managing a business or our own personal finances, we are often presented with
some choice in options for loans, deposits, and other investments. As borrowers, we want
to pay as little interest as possible, and so want to be able to find a low interest rate; as
lenders, the shoe is on the other foot and we want to seek out a high interest rate.
Of course, rates are not the only thing to consider. You probably would not choose to
open a savings account at a bank with inconvenient branches and rude customer service
just to earn a slightly higher rate on your account. But all other things being equal you want
to find the best rate you can.
Now, it would seem that comparing interest rates would be a fairly easy thing to do: if
you are borrowing go for the smallest percent, and if you are lending go for the highest.
And in some cases, it really is that simple. For example:Example 3.3.1 Which of the following banks is offering the best rate for a
certifi cate of deposit?Bank Rate Compounding
Maplehurst Savings and Loan 3.79% Annual
Killbuck First Financial 3¾% AnnualBoth rates are compounded annually, so for comparison we need only look at the rates. Since
3¾% 3.75%, it is not hard to see that Maplehurst S&L is offering a slightly higher rate.114 Chapter 3 Compound Interest
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