Question

what sum of money at compound interest will amount to 4499.04 in 3 years , if the rate of interest is 3% for the first year , 4% for the second year and 5% for the third year​

Answer 1

Answer:

Answer: A= Rs 4499.04/-

Step-by-step explanation:

Answer: A= Rs 4499.04/-

Answer 2

Step-by-step explanation:

Given :-

The sum of money at compound interest will amount to 4499.04 in 3 years , if the rate of interest is 3% for the first year , 4% for the second year and 5% for the third year.

To find :-

Find the sum of the money ?

Solution :-

Let the sum of the money be Rs. X

Principle (P) = Rs. X

Amount after 3 years (A) = Rs. 4499.04

Rate of Interest for the first year (R) = 3%

Time (T) = 1 years

Interest for the first year (I) = PTR/100

=> I = (X×1×3)/100

=> I = 3X/100

Interest for the first year = Rs. 3X/100

We know that

Amount = Principle + Interest

=> A = X+(3X/100)

=> A = (100X+3X)/100

=> A = 103X/100

Amount after first year = Rs. 103X/100

Given that

The amount is calculated compounded interest

So Principle for the second year = Rs. 103X/100

Rate of Interest = 4%

Interest for the second year

=> I = ((103X/100)×1×4)/100

=> I = (103X×4)/(100×100)

=> I = 412X/10000

=> I = 103X/2500

Interest for the second year = Rs. 103X/2500

Amount = P+I

=> A = (103X/100)+(103X/2500)

=> A = [(103X×25)+103X]/2500

=> A = (2575X+103X)/2500

=> A = 2678X/2500

=> A = 1339X/1250

Amount after second year = Rs. 1339X/1250

It will be the principle for the third year

Rate of interest = 5%

Interest for the third year = PTR/100

=> I = [(1339X/1250)×1×5]/100

=> I = (1339X×5)/125000

=> I = 1339X/25000

Interest for the third year = Rs. 1339X/25000

Amount = P+I

=> A = (1339X/1250)+(1339X/25000)

=> A = [(1339X×20)+(1339X)]/25000

=> A = (26780X+1339X)/25000

=> A = 28119X/25000

Amount after third year = Rs. 28119X/25000

But,

According to the given problem

Amount after 3 years (A) = Rs. 4499.04

=> 28119X/25000 = 4499.04

=> 28119X = 4499.04×25000

=> 28119X = 112476000

=> X = 112476000/28119

=> X = 4000

The Sum = Rs. 4000

Answer:-

The required sum of money for the given problem is Rs. 4000

Used formulae:-

• Simple Interest = PTR/100

• Amount = Principle + Interest

• P = Principle

• T = Time

• R = Rate of Interest

• A = Amount