Question

Equal sums of money were invested in scheme A and scheme B for two years. Scheme A offers simple interest and scheme B offers compound interest (compounded annually) and the rate of interest (p.c.p.a) for both the schemes are same. The interest accrued from Scheme A after two years is Rs. 2560/- and from scheme B is Rs. 2688/-. Had the rate of interest (p.c.p.a) of scheme A been 6% more, what would have been the interest accrued from Scheme A after two years?​

Answer 1

Answer:

Rs. 4096/-

Step-by-step explanation:

Let us assume that the sum of money is x Rs. and the interest rate is r% for both scheme A and B.

Given that the time of investment is 2 years for both schemes.

Also given,

For scheme A the interest rate is simple and the interest accrued is 2560 Rs.

For scheme B the interest rate is compound and the interest accrued is 2688 Rs.

Now, for scheme A,

interest accrued = $\frac{2x}{100} r=2560$

⇒$\frac{xr}{50}=2560$ ..... (1)

⇒$xr=128000$ .....(2)

Now, for scheme B,

interest accrued =$\frac{xr}{100}+\frac{(x+\frac{xr}{100} )}{100}r$=2688

⇒$\frac{2xr}{100}+\frac{xr^{2} }{10000}$=2688

⇒$\frac{xr}{50}+\frac{xr}{10000}r$=2688

⇒2560+$\frac{128000}{10000}r$=2688 {Using equation (1)}

⇒12.8r=128

⇒ r=10

So, the interest rate is 10%.

Now, from equation (2), x=$\frac{128000}{r}$=12800.

So, the invested sum is 12800 Rs.

If the interest rate is increased by 6% for the scheme A, i.e. (10+6)%=16%, then the interest accrued would have been after 2 years

=$\frac{2xR}{100}$ {Where, R=16% i.e. the new interest rate}

=$\frac{2*12800*16}{100}$

=4096 Rs. (Answer)