Question

in how many least number of complete years a sum of money become more than four times ofitself at the rate of 50 percent per annum on simple interest?

Answer 1

It will take at least 7 complete years for a sum of money to grow more than four times itself at a 50 percent per annum simple interest rate.

To determine the minimum number of complete years for a sum of money to become more than four times itself at a 50 percent per annum simple interest rate, we can use the formula for simple interest:

`\[ I = P \cdot r \cdot t \]`

where:

- I is the interest earned,

- P is the principal amount,

- r is the annual interest rate, and

- t is the time in years.

Given that the interest rate (r) is 50 percent (or 0.5) and the goal is for the sum to become more than four times itself, we can set up the inequality:

P + I > 4P

Now, substitute the formula for simple interest:

`\[ P + P \cdot r \cdot t > 4P \]`

Plug in the values:

1 + 1 · 0.5 · t > 4

Solve for t :

1 + 0.5t > 4

0.5t > 3

t > 6

So, it will take more than 6 years for the sum of money to become more than four times itself at a 50 percent per annum simple interest rate. Therefore, the minimum number of complete years is 7.