Finding Principal

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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
________________________________________________________________________
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 .
__________________________________________________________________
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

Home Page