A sum of ₹7,500 amounts to ₹8,748 after 2 years at a certain compound interest rate per annum. What will be the simple interest on the same sum for $$4\frac{3}{5}$$ years at double the earlier interest rate ?

let use this formula to find the rate of interest that is

Amount=principal (1+$$\frac{r}{100})^t$$

Given data in the question is 

Amount=8748

Principal=7500

Time=2years

Substitute above values in the formula then we will get

8748=7500(1+$$\frac{r}{100})^2$$

$$\frac{8748}{7500}$$=(1+$$\frac{r}{100})^2$$

Divide 8748 and 7500 by 12 then we get

$$\frac{729}{625}$$=(1+$$\frac{r}{100})^2$$

By eliminating square we get

$$\frac{27}{25}$$=(1+$$\frac{r}{100})$$

$$\frac{r}{100}$$=$$\frac{27}{25}$$-1

$$\frac{r}{100}$$=$$\frac{2}{25}$$

Rate of interest=$$\frac{100}{25}×2$$

Rate of interest=8

Therefore rate of compound interest=8%p.a

Now we have to find the simple interest for the sum ₹7500 for $$\frac{23}{5}$$ years at the rate=2×rate of interest

Rate of interest=2×8=16

Using the simple interest formula

Simple interest=$$\frac{principal×rate of interest ×time}{100}$$

Simple interest=$$\frac{7500×16×23}{5×100}$$

Simple interest=5520₹