Question

What sum of money lent at 6.5% per annum will produce the same interest in 4 years as Rs.7500 produce in 6 years at 5% per annum?

Answer 1

Given:

1. The first sum is lent at 6.5% per annum for 4 years.
2. The second sum is Rs. 7500 lent at 5% per annum for 6 years.
3. Both produce the same interest.

Step 1: Calculate the interest from the second sum

The formula for simple interest is:

`SI = (PxxRxxT)/100`

Substitute the values for the second sum:

`SI_2 = (7500xx5xx6)/100`

= Rs. 2250.

Step 2: Use the interest to find the first sum

`SI_1 = (P_1xxR_1xxT_1)/100`

Substitute SI₁ = Rs. 2250, R₁ = 6.5%, and T₁ = 4 years:

`2250 = (P_1xx6.5xx4)/100`

Rearrange to solve for P₁:

`P_1 = (2250xx100)/(6.5xx4) = 225000/26`

= Rs. 8653.85.