1. Finding P or n or r with Multiples

2. Recap on simple interest
Amount = Principal + Interest
Where n is in years

3. Amount = Principal + Interest
Example1 : - A certain sum of money amounts to Rs.10,080 in 5 years at 8 %.
Find the principal.
Solution Given: Amount(A)=10080 , no of years(n)= 5 , rate(r)= 8
To find: Principal(p)
We know that 2 20 5
Amount = Principal + Interest
1440
Ans: Principal = Rs 7200
p =1440 x 5 =7200

4. Example 2 A sum of money doubles itself in 10 years
Example 2 A sum of money doubles itself in 10 years. Find the rate of interest
Solution
Given: Period(n)=10 , A=double of principal=2P,
To find: Rate(r)
All value is given except value I. So lets find I
We Know that I=A-P = 2P-P=P (∵A=2P)
Ans: Rate (r) = 10% yearly

5. Example 3: A sum of money doubles itself at 10 % per annum over a certain time. Find the number of years.
Solution
Given: Rate(r)=10 , A=double of principal=2P,
To find: Rate(r)
All value is given except value I. So lets find I
We Know that I=A-P = 2P-P=P (∵A=2P)
Ans: Period(n) = 10 years

6. Example 4: A certain sum of money amounts to Rs 5,750 in years and Rs 6,500 in 3 years respectively . Find the principal and the rate percent.
Solution
Given: Period 1: Amount(A1)=5750, Period (n1) =
Period 2: Amount(A2)=6500, Period (n2) = 3
To find: Principal(P), Rate(r)
From period 1 to Period 2 Years passed=n2 - n1=
Interest earned = A2- A1= =750
In years Interest earned Rs 750

7. Ans: Principal(P)=Rs 5000 and Rate (r) = 10% yearly
Now lets calculate Interest(S.I2) ,Principal(P) and rate(r) based on period2
Interest earned in Period 2 (S.I2) = Interest per year x 3=500 x 3 =Rs 1500
We know that P = A2 - I2
∴ P = =Rs 5000
Ans: Principal(P)=Rs 5000 and Rate (r) = 10% yearly

8. Try these 1. A certain sum of money amounts to Rs.10,080 in 5 years
at 8 % . Find the principal.
2. Radhika deposited some money and it triples itself at 4%
per annum. Find the number of years.