Finding Principal

For finding principal we use the same formula of amount as

A = P( 1 + r)ⁿ

Where, P = principal
R = rate in percent

Examples :

1) What sum will become $9826 in 18 months if the rate of interest is 2 ½ % p.a. and the interest is compounded half-yearly ?

Solution :
Let the principal be $ P .
R = 2 ½ % = 5/2 % = 2.5 %
n = 18 months = 18/12 = 3/2 years
Amount = A = $ 9826
As the interest is compounded half yearly then
A = P ( 1 + r/2)²ⁿ
9826 = P( 1 + 0.025/2)^{2 x 3/2}
9826 = P(1 + 0.0125)³
9826 = P (1.0125)³
9826 = P x 1.03797
P = 9826/1.03797
P = $ 9466.55
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2) Find the principal, if the compound interest compounded annually at the rate of 10% p.a. for three years is $ 331.

Solution :
Let the principal be $ P.
Compound interest = C.I= $ 331
Rate in percent = 10
n = 3 years
C.I = A – P C.I = P( 1 + r)ⁿ - P
331 = P ( 1 + 0.10)³ - P
331 = P ( 1.10)³- P
331 = P x 1.331 – P
331 = 0.331 x P
P = 331/0.331
P = $ 1000 .
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3) Find the sum which will earn $164 as compound interest at 5% per annum for 2 years compounded annually.

Solution :
Let the principal be $ P .
R = 5 %
n = 2 years
CI = $ 164
As the interest is given
CI = A - P
2n - P
164 = P ( 1 + 5%)²ⁿ - P
164 = P [ (1 + 5%)²ⁿ - 1]
164 = P [ (1 + 0.05)²ⁿ -1]
164 = P[ (1.05)²ⁿ -1]
164 = P[ 1.1025 -1]
164 = 0.1025 P
P = 164/0.1025
P = $ 1600

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Compound Interest ( CI )

• Find Compound Interest when interest is compounded Half yearly
• Find Compound Interest when interest is compounded Quarterly
• Find CI when interest is compounded annually but Rates are different
• Finding Principal
• Finding Time Period of Investment
• Finding Rate of Interest

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