Question

A sum of money grows 216/125 times when invested for 3 years in shares where interest is computed annually. How long will the sum of money take to reach 5 times at the same rate of interest is compounded using simple interest method

Answer 1

Given :- A sum of money grows 216/125 times when invested for 3 years in shares where interest is computed annually .

To Find :- How long will the sum of money take to reach 5 times at the same rate of interest is compounded using simple interest method ?

Solution :-

Let us assume that,

• Principal = 125x .
• Rate = R% per annum compounded annually .
• Time = 3 years.
• Amount = (216/125) times of P = 216x .

we know that, when rate is compounded annually ,

• Amount = Principal * [1 + (Rate/100)]^(time)

So,

→ 216x = 125x[1 + (R/100)]³

→ (216/125) = [1 + (R/100)]³

→ (6/5)³ = [1 + (R/100)]³

→ [1 + (1/5)] = [1 + (R/100)]

→ [1 + (20/100)] = [1 + (R/100)]

comparing,

→ R = 20% .

Now, we have ,

• Principal = 125x
• Amount = 5 times = 125x * 5 = 625x .
• Simple interest = A - P = 625x - 125x = 500x .
• Rate = 20% .
• Time = ?

we know that, when rate is compounded using simple interest method ,

• SI = (P * R * T)/100

So,

→ 500x = (125x * 20 * T)/100

→ (500x * 100) = 2500x * T

→ 500 = 25T

→ T = 20 years. (Ans.)

Hence, It takes 20 years for the sum to reach 5 times when rate is at simple interest.

Learn more :-

A person invest two equal sums, one at simple interest and another at compound interest at same rate for two years. Afte...

https://brainly.in/question/27125261