# 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

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