A certain amount was deposited into a bank account having a simple interest rate of 5% . if the total amount 4 years was 1,500Rs how much was the amount deposited initially ? For the same initial amount ,how should the interest rate increase such that the simple interest would amount to 400Rs?
Answers
Step-by-step explanation:
Given :-
A certain amount was deposited into a bank account having a simple interest rate of 5% . if the total amount 4 years was Rs. 1,500
To find :-
How much was the amount deposited initially ? For the same initial amount ,how should the interest rate increase such that the simple interest would amount to Rs. 400?
Solution :-
Let the amount was deposited initially be Rs. X
Finding the Principle:-
Principle (P) = Rs. X
Rate of Interest (R) = 5%
Time (T) = 4 years
Amount after 4 years = Rs. 1500
We know that
Simple Interest = PTR/100
=> SI = (X×4×5)/100
=> SI = 20X/100
=> SI = X/5
Simple Interest = Rs. X/5
We know that
Amount = Principle + Interest
=> 1500 = X+(X/5)
=> 1500 = (5X+X)/5
=> 1500 = 6X/5
=> 6X/5 = 1500
=> 6X = 1500×5
=> 6X = 7500
=> X = 7500/6
=> X = 1250
Principle = Rs. 1250
The amount was deposited initially Rs. 1250
Finding Rate of Interest :
Given that
Simple Interest = Rs. 400
Let the increasing in the rate of interest be X%
The new rate of interest = (X+5)%
Principle = Rs. 1250
Time = 4 years
We know that
Simple Interest = PTR/100
=> 400 = (1250×4×(X+5))/100
=> (1250×4×(X+5))/100 = 400
=> 5000×(X+5) /100 = 400
=> 5000(X+5) = 400×100
=> 5000×(X+5) = 40000
=> X+5 = 40000/5000
=> X+5 = 40/5
=> X+5 = 8
=> X = 8-5
=> X = 3%
Increasing rate of Interest = 3%
Answer:-
1) The initial amount deposited in the bank is
Rs. 1250
2) The increasing in the rate of interest for the given problem is 3%
Used formulae:-
- Simple Interest = PTR/100
- P = Principle
- T = Time
- R = Rate of Interest
- Amount = Principle + Interest