Compound Interest Rate
A. Definition
Compound Interest Rate???
Answer :
The interest on a loan or deposit calculated
based on both the initial principal and the
accumulated interest from previous periods
Formula
S = P (1+i)n
i = jm/m
Note :
S = Total amount
P = principal
n = number of periods
m = frequency of interest rate
jm = nominal interest rate with calculation period m times per year
i = interest rate per interest calculation period
Factor (1+i)n is called Compound factor
Calculation process S from P is to find future value
Calculation process P from S s to find present value
Example
Compute compound interest rate from Rp 1.000.000 for
2 years with the rate10% p.a. and interest is calculated
semi-annually!
Answer :
Period
Principle
Compound
Total
1
Rp1.000.000
Rp1.000.000 x 0,05 =
Rp50.000
Rp1.050.000
2
Rp1.050.000
Rp1.050.000 x 0,05 =
Rp52.500
Rp1.102.500
3
Rp1.102.500
Rp1.102.500 x 0.05 =
Rp55.125
Rp1.157.625
4
Rp1.157.625
Rp1.157.625 x 0.05 =
Rp57.881,25
Rp1.215.506,25
S = P (1+i)n
Period 1 =
Rp 1.000.000(1+0.05)1 = Rp 1.050.000
Period
2 = Rp. 1.000.000 (1+0.05)2 = Rp 1.102.500
Period
3 = Rp. 1.000.000 (1+0.05)3 = Rp 1.157.625
Period
4 = Rp. 1.000.000 (1+0.05)4 = Rp 1.215.506,25
Exercise:
1.
How much S from P = Rp1.000.000 with compound interest rate j2
= 18% for 5 years?
2.
On her 20th birthday, Trinita received a prize of Rp10,000,000 as a
result of her father's savings since Trinita was born. How much
money did her father save when she was born if the interest rate
on savings did not change, with j2 = 6%?
3.
Mr. Tino saves his money Rp. 5,000,000 in a bank that pays 18%
interest per year where the interest is calculated monthly. How
much interest was earned during the first year?
Answer

No 1
Dik :
P = Rp1.000.000
i = 18% / 2 = 9% = 0.09
n = 5 x 2 = 10 period
S = P (1+i)n
S = Rp1.000.000 (1+0,09)10
S = Rp1.000.000 (2,367363675)
S = Rp2.367.363,675
Cont…

No 2
S = Rp10.000.000
i = 6% / 2 = 3% = 0,03
n = 20 x 2 = 40 period
S = P(1+i)n
10.000.000 = P(1+0,03)40
P = Rp10.000.000/(1+0.03)40
P = Rp3.065.568,4
Cont…

No 3
P = Rp5.000.000
i = 18% / 12 = 1,5% = 0,015
n = 12 period
S = P(1+i)n
S = Rp5.000.000 (1+0,015)12
S = 5.978.090,875
I =S–P
I = Rp5.978.090,875 – Rp5.000.000
I = Rp 978.090,875
B. Effective Interest Rate and Nominal
Interest Rate

The effective interest rate is the interest rate that
increases with the increasing frequency of multiplying
interest in a period

The nominal interest rate is the interest rate imposed
on the creditor or promised by the debtor.
Formula
j1 = (1+i)m – 1
or,
1+ j1 = (1+i)m
Where: j1 is the interest rate with the interest
calculation period once a year (annual)
Example
Calculate j4 that is equivalent with:
a) j12 = 12%
b) j2 = 10%
Answer :
a) (1+i)4 = (1+(0,12/12))12
i = (1+0.01)3 – 1
i = 1,030301 – 1
i = 0,030301
So j4 = 0,030301 x 4 = 0,121204 = 12,12%
Cont…
b) (1+i)4 = (1+(0,1 / 2))2
i = (1+0.05)1/2 – 1
i = 1,024695 – 1
i = 0,024695
So j4 = 0,024695 x 4 = 0,09878 = 9,88%
Exercise:
Calculate interest rate j1 that is equivalent with:
a) j26 = 13%
b) j365 = 24%
Answer :
a) (1+i)1 = (1+(0,13 / 26))26
i = 1,138459553 – 1
i = 0,138459553
so J1 = 0,138459553 x 1 = 0,138459553 = 13,85%
Cont…
b) (1+i)1 = (1+(0,24 / 365))365
i = 1,271148893 – 1
i = 0,271148893
so J1 = 0,271148893 x 1 = 0,271148893 = 27,11%