Unit 4: Simple Interest - Sample Problems
Example:
To buy a new computer, you take out a $3000 loan at 7% annual interest rate on February 15th. The loan is due
July 15th. The year is not a leap year. Round the answer to the nearest cent:
a) Find the ordinary interest that is paid in this loan.
Answer: To work this you need to first figure out how many days the loan is in effect. The textbook for this
course has a table the students can use; suggest they use that to look up the information. What they need to do is
figure out what day in the year February 15th is and what day in the year July 15th is, then subtract the smaller
number from the bigger. That will tell them how many days the loan is in effect. For this example, the table
values give us:
196 (for July 15th) - 46 (for February 15th) = 150 (caution students to not just use 30 days per month just
because some months do have 31 days (like January) so their figures will be off if they do that).
Now compute interest as follows: I = Prt, P = amount borrowed, r = rate of interest, t = time in years (assume
360 days in a year for ordinary interest).
So: I = 3000(.07)(150/360) = $87.50
b) Find the maturity value of the loan
By definition, the maturity value of a loan is the total of the principle + interest charged on the loan. For this
example, the principle is $3,000 and the interest is our answer found in part a, so the maturity value is $3,000 +
$87.5 = $3,087.5
Example:
You decide to make a payment of $5,000 on the 45th day of a $15,000, 210 day, 10% loan.
a) What is the adjusted principal after the payment is made if ordinary interest is applied?
Answer to a: You need to calculate the ordinary interest on 45 days, remember ordinary interest assumes a 360
day year:
Interest = $15,000 * (.1) * (45/360) = $187.50
Adjusted Principal is then: $15,000 + $187.50 - $5,000 = $10,187.50
b) What is the adjusted balance due at maturity (when the loan is due)?
Answer to b: Interest on adjusted principal (use your answer from a) is: $10,187.50 * (.1) * (165/360) =
$466.93. As for why you use 165/360 here, when the payment was made 45 days had already passed on the
loan, so there are 210 - 45 = 165 days left to charge interest on.
Therefore, the grand total owed on this loan when the loan comes due is now: $10,187.50 + $466.93 =
$10,654.43
Example:
A local business needs to replace a crane for factory work. The business was able to work out a deal with a
vendor to get the crane for $6,750, plus sales tax of 6.5%. The cash terms of the purchase are 2/20, n/45, with a
5% service charge on late payments, or a 90 days same as cash if they put it in the company credit card. The
credit card comes with a payment plan of 27% for the first 90 days, then 27% interest per year thereafter.
a) If the business takes the cash option and pays it off within the discount period (20 days in this example) how
much will it save?
Answer to a: The business will save 2% off of the purchase price. Remember that we calculate the discount on
only the purchase price, not on the purchase prices plus sales tax. To figure out the amount of the discount,
compute as follows:
$6,750 * .02 = $135 total saved by paying within 20 days if they use the cash option.
b) If the business buys the crane on December 1st and uses the 90 days same as cash, how long do the business
have to pay it off? Use exact time in figuring the answer.
Answer to b: Exact time means you need to figure out precisely when 90 days are from December 1st.
December has 31 days, January has 31, and Feburary has 28 (non leap year). So December 1st to January 1st
(31) + time from January 1st to February 1st (31 more) = 62 days so far. So 28 days are left, and that means
since February has 28 days the same as cash payment is due somewhere in the month of February.
To get the exact date, when you get to February there are 28 days left, so that means the payment is due on
February 28th. So February 28th is the answer.
Note that we can also solve the problem using the tables which list days of the year that have passed; you would
need to figure out how many days December 1st is from the end of the year (31) then take 90 - 31 = 59 which
tells you that the 90 days same as cash ends when the 59th day of the year is (findable using a table).
c) If the business does the 90 days same as cash and pays off before February 28th, what is its payoff amount?
If it cannot pay the bill until March 20th what is its payoff amount now?
Answer to c) First of all you need to figure out the total the business would owe if it uses this option. The
company is responsible for the purchase price (6750) plus the sales tax of 6.5%. So the total the business owes
is $6,750 + (.065)($6,750) = $6,750 + $438.75 = $7,188.75, which is what they owe if they pay it off within the
90 days.
At the end of the 90 days, if they do not pay off the balance, they are charged interest of 27% for the previous
90 days (Note that this is normal practice on those same as cash offers; they charge interest on the entire balance
for the entire period of the same as cash time period if it is not paid off in time). The amount you would
compute as follows:
$7,188.75 (total owed) * .27 (interest) * (90/360) (we use 360 here as most businesses use 360 or ordinary
interest on consumer loans) = $485.24 charged in deferred interest, so the total now due after the 90 days pass is
$7,188.75 + $485.24 = $7,673.99 now due when the 90 days expire on Feburary 28th.
The question wants to know how much is due on March 20th, when the business can pay off the loan. So we
need to figure out how many days there are from February 28th to March 20th. There are 20 days from
February 28th to March 20th so interest will be charged from February 28th until March 20th. Therefore they
owe another: $7,673.99 * .27 * (20/360) in interest, or $115.11 in interest charged additionally
So therefore the grand total of what they pay is $7,673.99 * 115.11 = $7,789.10 total owed
Author’s note: Please note that by the new credit card laws most companies would not charge interest on that
last month. However do not overanalyze the problem that way and just compute it as raw interest. Adding in
details like the legal rules on credit cards and how they apply to what is due are topics for another class, so
disregard them for now.
d: The business has the option to get a local 90 day promissory note at a local bank for $7500 at 8% interest. Is
this enough money to cover the purchase of the crane? Is this a better option to pursue? What would you do in
this position?
Answer to d: Answers vary, but you can at least work the amount gained by the bank promissory note. The way
the note works is the borrower gets $7,500 minus the amount of interest of the loan, and pays $7500 in 90 days.
So the total the person borrowing this note at 8% would receive is:
$7,500 - (.08)(90/360)7500 = $7,500 - 150 = $7,350. So they would receive $7,350 in cash to use, and lose
$150 in interest to the bank when they pay back the $7,500. Rest of answers would vary, as it depends on when
in this process they get the note.