if the simple interest on a certain principal for 3 years at 10% p.a. is less than its simple interest at 9% p.a. for 4½ years by 1,260 find the principal amount
Answers
Answer:
Rs 6,300
Step-by-step explanation:
Simple Interest, S.I. = Rs. 1260 =
100
PR×2
=
50
PR
-(i)
Compound Interest, C.I. = Amount(A) - Principle(P)
=P(1+
100
R
)
2
- P = PR(R/10000+1/50)=Rs.1323 -(ii)
Dividing (ii) by (I),
200
R
+1 =
1260
1323
⇒Rate,R=10%p.a.
Now,
100
PRT
=1260
⇒
100
P×10×2
=1260
⇒ Principal or Sum , P = Rs.6,300
Concept
Simple interest (S.I) is a method of calculating the amount of interest for a certain amount of money.
The formula for simple interest helps you find the amount of interest if the principal amount, interest rate, and time period are given.
A simple interest formula is given as follows:
I=PRN
Where I = simple interest
P = Principal amount
R = interest rate (in percent)
N = duration (in years)
Given
It is given that the simple interest on a certain principal for 3 years at 10% p.a. is less than its simple interest at 9% p.a. for 4½ years by 1,260
Find
We need to find the principal amount
Solution
simple interest on a certain principal for 3 years at 10% p.a. is less than its simple interest at 9% p.a. for 4½ years by 1,260
R1=9% , N1=4½ years =9/2 years
R2=10% , N2=3 years
I1 - I2 = 1260
P*R1*N1 - P*R2*N2 = 1260
P*9/100*9/2 - P*10/100*3 = 1260
P(81/200 - 3/10) =1260
P((81-60)/200)=1260
P= 1260*200/21
P=Rs.12000
Hence the principal amount is Rs 12000
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