Power point presentation about Simple and Compound Interest

2. -may be defined as the charge for
using the borrowed money. It is an
expense for the person who borrows
money and income for the person who
lends money. Interest is charged on
principal amount at a certain rate for a
certain period. For example, 10% per
year, 4% per quarter or 2% per month
etc.

3. Principal amount means the amount of
money that is originally borrowed from an
individual or a financial institution. It does not
include interest. In practice, the interest is
charged using one of two methods. These are:
1. simple interest method; and
2. 2. compound interest method

4. Under this method, the interest is charged only on
the amount originally lent (principal amount) to the
borrower. Interest is not charged on any
accumulated interest under this method. Simple
interest is usually charged on short-term borrowings.

5. Simple interest can be easily
computed using the following
formula: I = Prt
Where;
• I = Simple interest
• P = Principal amount
• i = rate of interest
• n = time/number of periods

6. Example 1: A person deposits 5,000.00 in a bank
account which pays 6% simple interest per year.
Find the value of his deposit after 4 years.
Solution : Formula for simple interest is I = Prt
Here, P = 5000, t = 4, r = 6%
Let us plug these values in the above formula
I = 5000 ⋅ 6/100 ⋅ 4
I = 1200

7. The formula to find the accumulated value is
= Principal + Interest
= 5000 + 1200
= 6200
Hence, the value of his deposit after 4 years is
6,200.00.

8. Compounding of interest is very common. Under
this method, the interest is charged on principal
plus any accumulated interest. The amount of
interest for a period is added to the amount of
principal to compute the interest for next period. In
other words, the interest is reinvested to earn
more interest.

9. The interest may be
compounded monthly, quarterly,
semiannually or annually.
Consider the following example
to understand the whole
procedure of compounding.

10. Example 1: Suppose, you have deposited 100.00 with
a bank for five years at a rate of 5% per year
compounded annually. The interest for the first year
will be computed on 100.00 and you will have 105.00
(100.00 principal + 5.00 interest) at the end of first
year. The interest for the second year will be
computed on 105.00 and at the end of second year
you will have 110.25 (105 principal + 5.25 interest).
The interest for the third year will be computed on
110.25 and at the end of third year you will have
115.76 (110.25 principal + 5.51 interest). The
following table shows the computation for 5-year
period of investment.

11. Year Principal
Amount
Rate of
Interest
Interest Compound
Amount
1 100.00 5% 100.00 × 0.05
= 5.00
100.00 + 5.00
= 105.00
2 105.00 5% 105.00 × 0.05
= 5.25
105.00 + 5.25
= 110.25
3 110.25 5% 110.25 × 0.05
= 5.51
110.25 + 5.51
= 115.76

12. 4 115.76 5% 115.76 ×0.05 =
5.79
115.76 + 5.79
= 121.55
5 121.55 5% 121.55 × 0.05
= 6.08
121.55 + 56.08
= 127.63

13. Under compound interest system, when interest is
added to the principal amount, the resulting figure is
known as compound amount. In the above table,
the compound amount at the end of each year have
been computed in the last column. Notice that the
compound amount at the end of a year becomes the
principal amount to compute the interest for the next
year.

14. Compound amount and compound interest formula:
The above procedure of computing compound
amount and compound interest is lengthy and time
consuming. Fortunately, the formulas are available
to compute compound amount and compound
interest for any number of periods.
(i) Compound amount formula: A = P(1 + i)

15. Where;
• A = Compound amount
• P = Principal amount
• i = rate of interest
• n = number of periods

16. Compound interest = Compound amount –
Principal amount
Example 2: The City Bank has issued a loan of
10,000.00 to a sole proprietor for a period of 5-years.
The interest rate for this loan is 5% and the interest is
compounded annually. Compute
1. compound amount
2. 2. compound interest

17. 1.Computation of Compound
Amount:
A = P(1 + i)n
= 10,000 × (1 + 5%)5
= 10,000 × (1 + .05)5
= 10,000 × (1.05)5
= 10,000 × 1.276
= 12,760.00

18. 2. Computation of Compound Interest: Once the
compound amount has been computed, the amount of
interest earned over the investment period can be
computed by subtracting principal amount from the
compound amount. In this example, the principle
amount is 10,000 and the compound amount
computed above is 12,760.00. The amount of
compound interest for the fiver year period can be
computed as follows:
Compound interest = Compound amount – Principle
amount
= 12,760.00 – 10,000.00
= 2,760.00

19. Use of future value of $1 table to compute
compound amount: (see Appendix A)
The shortest and easiest method to compute
compound amount is to use the future value of $1
table (See Appendix 1). This table contains the value
of (1 + i)n for a given value of i and n. After locating
the value of (1 + i)n in the table, the principal amount
is simply multiplied with the value to find the
compound amount. The principal amount is then
subtracted from compound amount to get the
amount of compound interest for the given interest
rate and time period.

20. = 10,000.00 × (1 + 5%)5
= 10,000.00 × 1.276*
= 12,760.00
Compound interest: 12,760.00 – 10,000.00
= 2,760.00
*Value of (1 + 5%)5 from future value of $1 table: 5
periods; 5% interest rate. The future value tables
are widely used in accounting and finance to save
time and avoid unnecessary computations.

21. Compound interest is greater than simple
interest:
Compound interest is greater than simple
interest. The reason is very simple. Under
simple interest system, the interest is
computed only on principal amount whereas
under compound interest system, the interest
is computed on principle as well as on
accumulated interest.

22. End!!!