1. CHAPTER 3 COMPOUND INTEREST
REV 00
CHAPTER 3
COMPOUND INTEREST
DDG 1113
BUSINESS MATHEMATICS

2. REV 00
3.1 TIME VALUE OF MONEY
Money has time value, that is a ringgit today is worth more than a ringgit tomorrow.
Money has time value because of its investment opportunities.
DDG 1113
BUSINESS MATHEMATICS

3. REV 00
3.2 COMPOUND INTEREST
In compounding, after the interest is calculated, it is then added to the principal and becomes an adjusted principal.
Processes are repeated until the end of the loan or investment term.
Normally used with long-term loan or investment, and the interest is calculated more than once during the loan or investment term.
DDG 1113
BUSINESS MATHEMATICS

4. REV 00
The interest earned is called compound interest, and the final sum at the end of the period of borrowing is called the compound amount.
Therefore, compound interest is the difference between the original principal and the amount.
DDG 1113
BUSINESS MATHEMATICS

5. REV 00
3.3 SOME IMPORTANT TERMS
Some of the common terms used in relation to compound interest are:
1. Original principal
2. Nominal interest rate
3. Interest period or conversion period
4. Frequency of conversions
5. Periodic interest rate
6. Number of interest periods in the investment
period
DDG 1113
BUSINESS MATHEMATICS

6. 3.4 COMPOUND INTEREST FORMULA
REV 00
3.4 COMPOUND INTEREST FORMULA
The method used in finding compound amount at the end of the nth period is as follow:
S = P(1 + i)n
Where:
P = Principal / Present Value
S = Future Value
n = Number of Periods (number of years multiplied by number of times compounded per year)
i = Interest rate per compound period
DDG 1113
BUSINESS MATHEMATICS

7. Example 1 pg 41 Find the future value of RM 1000 which was invested for a) 4 years at 4% compounded annually, b) 5 years 6 months at 14% compounded semi annually, c) 2 years 3 months at 4% compounded quarterly d0 5 years 7 months at 5% compounded monthly e) 2 years 8 months at 9% compounded every 2 months f) 250 days at 10% compounded daily.
DDG 1113
BUSINESS MATHEMATICS

8. Example 2 pg 42
RM 9000 is invested for 7 years 3 months. This investment is offered 12% compounded monthly for the first 4 years and 12% compounded quarterly for the rest of the period. Calculate the future value of this investment.
Example 3 pg 42
Lolita saved RM 5000 in a saving account which pays 12% interest compounded monthly. Eight months later she saved another RM Find he amount in the account two years after her first saving.
Example 4 pg 43
What is the nominal rate compounded monthly that will make RM 1000 become RM 2000 in five years?
DDG 1113
BUSINESS MATHEMATICS

9. 3.5 EFFECTIVE, NOMINAL AND EQUIVALENT RATES
REV 00
3.5 EFFECTIVE, NOMINAL AND EQUIVALENT RATES
Effective rate : Simple rate that will produce the same accumulated amount as the nominal rate is compounded each period after one year.
Nominal rate : Stated annual interest rate at which interest is compounding more than once a year.
Equivalent rate : Two different rates that yield the same value at the end of one year.
DDG 1113
BUSINESS MATHEMATICS

10. 3.6 RELATIONSHIP BETWEEN EFFECTIVE AND NOMINAL RATES
REV 00
3.6 RELATIONSHIP BETWEEN EFFECTIVE AND NOMINAL RATES
The relationship between the nominal rate and effective rate is derived as follows:
Assume a sum RM P is invested for one year. Then the future value after one year:
(a) At r% effective = P(1 + r)
(b) At k% compounded m times a year = P(1 + k/m)m
DDG 1113
BUSINESS MATHEMATICS

11. Example 1 pg 41 Find the effective rate which is equivalent to 16% compounded semi annually. Example 2 pg 45 Find the nominal rate, compounded monthly which is equivalent to 9% effective rate. Example 3 pg 45 Kang wishes to borrow some money to finance some business expansion. He has received two difference quotes: Bank A: Charged 15.2% compounded annually Bank B: Charged 14.5% compounded monthly. Which bank provides a better deal?
DDG 1113
BUSINESS MATHEMATICS

12. 3.7 RELATIONSHIP BETWEEN TWO NOMINAL RATES
REV 00
3.7 RELATIONSHIP BETWEEN TWO NOMINAL RATES
The relationship between two nominal rates is given as follows:
(1 + k/m)m + (1 + K/M)M
Where:
k and K are two different annual rates with respectively two different frequencies of conversions, m and M.
DDG 1113
BUSINESS MATHEMATICS

13. Example 1 pg 46 Find K% compounded quarterly which is equivalent to 6% compounded monthly.
DDG 1113
BUSINESS MATHEMATICS

14. REV 00
3.8 PRESENT VALUE
Present value or discounted value is the value which will yield the sum (S) after certain time and at a specific interest rate.
We can find present value by transposing the formula as below:
S = P(1 + i)n
P = S / (1 + i)n or P = S(1 + i)-n
transpose
DDG 1113
BUSINESS MATHEMATICS

15. Example 1 pg 47 A debts of RM 3000 will mature in three years’ time
Example 1 pg 47 A debts of RM 3000 will mature in three years’ time. Find a) the present value of this debts b) the value of this debt at the end of the first year c) the value of this debts at the end if four years. Assuming money is worth 14% compounded semi annually. Example 2 pg 49 A debt of RM 7000 matures at the end of the second year and another of RM 8000 at the end of six years. If the debtor wishes to pay his debts by making one payment at the end of the fifth year, find the amount he mist pay if money is worth 6% compounded semi annually using a) the present as the focal date b) the end of the fifth year as the focal date.
DDG 1113
BUSINESS MATHEMATICS

16. Example 3 pg 50 A debt of RM 7000 matures at the end of the second year and another RM 8000 at the end of six years. If the debtor wishes to pay his debts making two equal payments at the end of the fourth year and the seven year, what are these payments assuming money is worth 6% compounded semi annually. Example 4 pg 51 Roland invested RM at 12% compounded monthly. This investment will be given to his three children when they reach 20 years old. Now his three children are 15, 16 and 19 years old. If his three children will receive equal amounts, find the amount each will receive.
DDG 1113
BUSINESS MATHEMATICS

17. REV 00
3.9 EQUATION OF VALUE
An equation that expresses the equivalence of two sets of obligations at a focal date.
In other words, it expresses the following:
What is owed = What is owned at the focal date or
What is given = What is received at the focal date
DDG 1113
BUSINESS MATHEMATICS

18. 3.10 CONTINUOUS COMPOUNDING
We have been discussing compounding of interest on discrete time intervals (daily, monthly, etc).
If compounding of interest is done on a continuous basis, then we will have a different picture of the future value as shown below:
Continuous compounding
Discrete compounding
Future value
Future value
Time
Time
DDG 1113
BUSINESS MATHEMATICS