A certain sum was put on simple interest at 20% per annum for 2 years. then the amount received after 2 years put on compound interest 15% per annum for 2 more years. if the amount received at the end of 4 year is 34450.find the amount invested???
Answers
Step-by-step explanation:
Given:-
A certain sum was put on simple interest at 20% per annum for 2 years. then the amount received after 2 years put on compound interest 15% per annum for 2 more years. if the amount received at the end of 4 year is 34450.
To find:-
Find the amount invested?
Solution:-
Let the amount be invested = Rs. P
Principle = Rs. P
Rate of Interest (I) = 20%
Time (T)=2 years
We know that Simple Interest (I) = PTR/100
=>I = (P×2×20)/100
=>I = 40P/100
=>I = 2P/5
Simple Interest after two years = Rs. 2P/5
Amount = Principle+ Interest
=>Amount = P+(2P/5)
=>Amount = (5P+2P)/5
Amount = Rs. 7P/5
Then if it is invested again then
Principle (P) =Rs. 7P/5
Rate of interest (R)=15%
Time (T)=2 years
Number of times the compound interest is calculated (n)=2 years
We know that
Amount (A) = P[1+(R/100)]^n
=>A = (7P/5)[1+(15/100)]^2
=>A = (7P/5)[1+(3/20)]^2
=>A = (7P/5)[(20+3)/20]^2
=>A = (7P/5)×(23/20)^2
=>A = (7P/5)×(23/20)×(23/20)
=>A = (7P×23×23)/(5×20×20)
=>A = 3703P/2000
Amount received at the end of 4 years
= Rs. 3703P/2000
According to the given problem
Amount received at the end of 4 years
=Rs.34450
=>3703P/2000 = 34450
=>3703P = 34450×2000
=>3703P = 68900000
=>P = 68900000/3703
=>P = 18606.535...
=>P = Rs. 18606.54
Answer:-
The Amount invested for the given problem is
Rs . 18606.54
used formulae:-
- Simple Interest (I) = PTR/100
- Amount = Principle+ Interest
- Amount (A) = P[1+(R/100)]^n