0
$\begingroup$

If an amount is kept at SI, it earns an interest of Rs.$600$ in the first two years but when kept at CI, it earns an interest of Rs $660$ in the same period. Find the rate of interest and the Principal.

The solution given is:- Rs $60$ is earned extra is the interest of first year. And since interest earned in all years is constant hence, interest earned is 300. Rate of interest= $60/300*100=20%$ At 20% interest of first year is Rs. 300. Thus, the principal is $300*100/20$=$1500$

  • 0
    Yes, SI is simple interest and CI is compound interest @LaarsHelenius – 2017-01-09
  • 0
    @LaarsHelenius I have edited the question. If you can explain me a bit how to find it using this one – 2017-01-09

3 Answers 3

1

Easiest way -

For each year SI equal throughout.

So for 2 years SI is 600 and for 1 year SI is 300.

For first year SI and CI are equal. So CI is 300.

After 2 year difference in CI and SI is 60.

In CI we get interest principle and on interest of the previous year.

For first year CI is 300 and for second year CI is 360.

In which 300 is interest on principle and 60 is interest on interest of first year. Time is 1 year.

$\frac{P \times R \times T}{100} = 60$

$\frac{300 \times R \times 1}{100} = 60$

On solving R = 20%.

For Principle -

As SI is 600. Using SI formula.

$\frac{P \times R \times T}{100} = 600$

$\frac{P \times 20 \times 2}{100} = 600$

P = 1500

  • 0
    If you understand the logic these questions are of one step questions. So please ask if not understand anything. – 2017-01-16
  • 0
    I did not understand the logic @KanwaljitSingh – 2017-06-10
0

Hint:

$\frac{2PR}{100}=600$ and $p(1+R/100)^2=660$

Two equations and two vaiables

  • 0
    That I got it but I wanted to solve this question by a more easier method @THELONEWOLF – 2017-01-09
  • 0
    @beginnercoder Then perhaps you should say what you've done, and what exactly it is you're looking for, in the body of the question. – 2017-01-09
  • 2
    @beginnercoder, AFAIK, this is the easiest method. – 2017-01-09
  • 0
    @pjs36 I have edited the question. If you can explain me a bit how to find it using this one – 2017-01-09
0

$2Pr = 600\\ P[(1+r)^2 -1] = 660$

You must subtract 1 if you just want the interest in the compound interest calculation. Leaving that out gives you the value of your investment (principal + interest) and the end of the period

$P(2r + r^2) = 660\\ 2Pr + Pr^2 = 660$

substitute

$600 + Pr^2 = 660\\ Pr^2 = 60\\ (Pr) r = 60$

substitute again

$300r = 60\\ r = 0.2$

$P(0.2) = 300\\ P = 1500$

  • 0
    I have edited the question, if you can explain me this way as given in the solution. – 2017-01-09
  • 0
    I have edited the question, if you can explain me this way as given in the solution. – 2017-01-10