Problems 679
Problems
20.1. Compute the future value of the following deposits
made today:
a. $10,000 at 6.75% compounding annually for
10 years
b. $10,000 at 6.75% compounding quarterly for
10 years
c. $10,000 at 6.75% compounding monthly for
10 years
20.2. Compute the interest earned on the deposits made in
Problem 20.1.
20.3. How much money do you need to deposit in a bank
today if you are planning to have $5000 in four
years by the time you get out of college? The bank
offers a 6.75% interest rate that compounds
monthly.
20.4. How much money do you need to deposit in a bank
each month if you are planning to have $5000 in four
years by the time you get out of college? The bank
offers a 6.75% interest rate that compounds monthly.
20.5. Determine the effective rate corresponding to the fol-
lowing nominal rates:
a. 6.25% compounding monthly
b. 9.25% compounding monthly
c. 16.9% compounding monthly
20.6. Using Excel or a spreadsheet of your choice, create
interest – time factor tables, similar to Table 20.8, for
i6.5% andi6.75%.
20.7. Using Excel or a spreadsheet of your choice, create
interest – time factor tables, similar to Table 20.8, for
i7.5% andi7.75%.
20.8. Using Excel or a spreadsheet of your choice, create
interest – time factor tables, similar to Table 20.8, for
i8.5% andi9.5%.
20.9. Using Excel or a spreadsheet of your choice,
create interest – time factor tables, similar to Table
20.8, that can be used fori8.5% compounding
monthly.
20.10.Most of you have credit cards, so you already know that
if you do not pay the balance on time, the credit card
issuer will charge you a certain interest rate each
month. Assuming that you are charged 1.25% interesteach month on your unpaid balance, what are the
nominal and effective interest rates? Also, determine
the effective interest rate that your own credit card
issuer charges you.
20.11. You have accepted a loan in the amount of $15,000
for your new car. You have agreed to pay the loan back
in four years. What is your monthly payment if you
agree to pay an interest rate of 9% compounding
monthly? Solve this problem for i 6%, i 7%, and
i 8%, each compounding monthly.
20.12.How much money will you have available to you after
five years if you put aside $100.00 a month in an
account that gives you 6.75% interest compounding
monthly?
20.13.How long does it take to double a deposit of $1000
a. at a compound annual interest rate of 6%
b. at a compound annual interest rate of 7%
c. at a compound annual interest rate of 8%
d. If instead of $1000 you deposit $5000, would the
time to double your money be different in parts
(a)–(d)? In other words, is the initial sum of money
a factor in determining how long it takes to double
your money?
Now use your answers to verify a rule of thumb that is
commonly used by bankers to determine how long it
takes to double a sum of money. The rule of thumb
commonly used by bankers is given by20.14.Imagine that as an engineering intern you have been
assigned the task of selecting a motor for a pump.
After reviewing motor catalogs, you narrow your choice
to two motors that are rated at 1.5 kW. Additional
information collected is shown in an accompanying
table. The pump is expected to run 4200 hours every
year. After checking with your electric utility company,
you determine the average cost of electricity is about
11 cents per kWh. Based on the information given here,
which one of the motors will you recommend to be
purchased?time period to double a sum of money
72
interest rate
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