COMPOUND INTEREST BY USING THE FORMULA –
1) When interest is compounded annually
a) let Principal = $ P, Rate = R % per annum, and Time = n years. Then,
R
Amount = $ { P ( 1 + ------- )ⁿ }
100
C.I = (Amount) – (Principal)
R
= $ [ P X { ( 1 + ------- )ⁿ - 1 } ]
100
Example.1) Calculate the amount and the compound interest on $ 15000 for 2 years at 10% per annum, compounded annually.
Ans.) Given P = $ 15000, R = 10% p.a, n = 2 years
R
Amount = P ( 1 + ------- )ⁿ
100
10
= $ { 15000 ( 1 + ------ )² }
100
110 110 110
= $ { 15000 X ( ------- )² } = $ { 15000 X ------- X ------- }
100 100 100
= $ ( 150 X 11 X 11 ) = $ 18150
Compound Interest (C.I) = Amount (A) – Principal (P)
= $ ( 18150 – 15000 ) = $ 3150
So, required amount (A) = $ 18150, and Compound Interest (C.I) = $ 3150 (Ans.)
Example.2) What sum of money will amount to $ 9680 in 2 years at 10% per annum compounded annually.
Ans.) As we know the formula –
R
Amount = $ { P ( 1 + ------ )ⁿ }
100
Here, as per given condition Amount (A) = $ 9680, Rate (R) = 10%, n = 2, and now we have to find principal (P) = ?
R
Amount = $ { P ( 1 + ------ )ⁿ }
100
10
9680 = P ( 1 + ------- )²
100
11
9680 = P X ( ------- )²
10
( 11 X 11 ) P
9680 = ---------------
10 X 10
9680 X 100
P = --------------- = $ 8000
121
So, here the required sum is $ 8000. (Ans.)
Example.3) The difference between the compound interest and the simple interest on a certain sum at 9% per annum for 2 years is $ 324, find the sum.
Ans.) let the required sum be $ a
Given, Rate (R) = 9% p.a, and Time = 2 hours
P X R X T 9 9a
As per the formula, S.I = ----------- = $ ( a X ---- X 2 ) = -----
100 100 50
9 109 X 109
C.I = $ { a ( 1 + ------ )²- a } = $ { a ( ------------ - a }
100 100 X 100
(109 X 109)a – (100 X 100) a
C.I = $ { ------------------------------ }
100 X 100
1881 a
= $ ------------
10000
1881 a 9 a 1881 a – 1800 a
C.I – S.I = $ ( -------- - ------- ) = ( --------------- )
10000 50 10000
81 a
= ---------
10000
But, this difference is given as $ 324
81 a
So, ---------- = $ 324
10000
324 X 10000
So, a = --------------- = $ 40000
81
Hence the required sum is $ 40000 (Ans.)