TUTORIAL 9
BUSINESS MATHEMATICS
MARCH 2003
Concept: Simple interest (BUD pp. 303 )
Simple interest is computed with the formula:
I = Pin,
Where, I = simple interest, P = principal, i = interest rate per time period, n = number of time periods of loan
Amount at end of period, A = P + Pin = P(1 +
in)
Example 1:
You have taken a loan of $10,000, for which simple interest is charged at 5% per year. If you repay the entire loan at the end of 2 years, how much did you repay?
Answer:
I = ?, P = 10,000, i = 5%, n = 2
I = 10,000 X 0.05 X 2 = 1000; repaid 10,000 + 1,000 = 11,000
OR
A = P + Pin = 10,000 + 10000 X 0.05 X 2 = 11,000
1.) Find n:
a.) 1.125n = 5,000
b.) 1.04n = 20,000
2.) $2,000 is invested at an interest rate of 6.5% for:
a.) Two years
b.) Four years
Find the simple interest earned.
3.) A businessman invests $10,000, and earns simple interest of $432 in the first half of the year. Find his annual rate of interest
4.) A firm obtains a loan of $150,000 for 8 months, at a simple interest rate of 10.5%. How much should the firm repay?
5.) Find the total amount due on a loan of RM1800 at 15% simple interest at the end of 3 months.
6.) Find the interest earned on RM5000 loaned out at an annual rate of 9% for 9 months.
7.) A firm paid interest of RM480 for a 3-month loan of RM8,000. What is the annual interest rate?
8.) In how many months will the interest on a loan of RM18,000, at an annual interest rate of 12%, come up to RM2700?
9.) How much is the interest on $4380 for 150 days at 11% interest?
10.) A student purchases a computer priced at RM1,500. He pays RM1620 six
months later, in full payment of the initial amount plus interest. Find the interest rate.
Compound interest rate is given by:
S = P(1+i) n
where,
S = compound amount
P = principal
i = interest rate per compounding period
n = number of compounding periods
Example:
You invest RM2000 in a savings account which earns interest at a rate of 4% per year compounded annually.
Find the compound amount after 8 years.
Answer:
S = P(1+i) n
where S = ?, P = 2000, i = 4%, n = 8
S = 2,000 (1+0.04) 8 = $2737.14
Financial calculator solution:
MODE: FIN
Set decimal to 2 places
8 = n
2,000 = PV
4 = i (note: enter direct %, do not change to decimal)
COMP FV
11.) How long will it take RM5000 to grow to RM6000 when it is invested at 9%
compounded monthly?
12.) If RM 2000 is invested at 4% compounded (i) annually (ii) semi-annually (iii)
quarterly (iv.) monthly,
Find the amount after 5 years (to the nearest sen)
13.) A worker places RM5000 in an employee’s savings account that pays 5%
simple interest. How long will it be until the investment amounts to RM5300?
14.) How many years will it take for RM10,000, compounded annually at 7%, to
reach RM15,000?
15.) Find the rate of interest compounded semi-annually at which RM15,000 will
grow to $20,000 in 10 years
16.) How many years will it take for a sum of money to triple at 8% compounded
annually?
17.) Find the rate of interest compounded monthly at which RM18,000 will grow to
RM24,000 in six years.
18.) Find the effective rate of 6% compounded annually, semi-annually, quarterly,
monthly, weekly and daily.
19.) What nominal interest rate compounded quarterly gives an effective rate of
8.5%?
20.) Which is a better investment and why: 9% compounded monthly or 9.3%
compounded annually?
21.) A debtor can discharge his liabilities by paying RM19,000 now or RM20,000 in
two years. If money is only worth 10% compounded semiannually, which is better?
22.) A businessman deposits RM5,000 in a bank account at the beginning of every
year for five years. If these deposits earn an interest of 5% compounded annually, how much will be in the bank account at the end of five years?
Independent study: BUD Chapter 8
