A certain sum of money becomes seven times itself when invested at a certain rate of simple interest, in 14 years. How much time (in years, rounded off to 2 decimal places) will it take to become 18 times itself at the same rate?

Question

Accepted Answer

Let the principal be P and the rate of simple interest be R% per annum.

Given: Amount after 14 years = 7P
So, Simple Interest (SI) = 7P - P = 6P

Simple Interest formula: SI = (P × R × T)/100
So, 6P = (P × R × 14)/100
=> 6 = (R × 14)/100
=> R = (6 × 100)/14 = 600/14 = 42.8571% per annum

Now, we want the sum to become 18 times itself.
So, Amount = 18P
SI = 18P - P = 17P

Using SI formula again:
17P = (P × R × t)/100
=> 17 = (R × t)/100
We already found R = 42.8571
So,
17 = (42.8571 × t)/100
=> t = (17 × 100)/42.8571
=> t ≈ 1700/42.8571 ≈ 39.67 years

Thus, the answer is 39.67 years.

Answer

Answer

Answer