# Finding Principal

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**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

• 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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