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Here's my problem : If the compound interest on a sum of money for 3 yr at the rate of 5% per annum is Rs 252.20, the simple interest on the same sum at the same rate and for the same time is ?

Can you please elaborate how to solve this question. I was thinking of an approach that if I do the following: 1) Take the CI given and then divide it by 100*100/105*105, thinking that would give me the CI after 1 year. 2) After I get the CI after an year, I simply would multiply that by 3 and get the SI for 3 years.

Where am I wrong. And if there are any alternate approaches they're welcome. Thanks

Nikhil Sharma
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  • So what you're saying is that using the compound interest formula and $t=3, r=.05, A=252.2$ Are you looking for $P$? and then you need to plug that into the simple interest formula with the already given $t$ and $r$ to find the $A_1$? – Fmonkey2001 Nov 24 '14 at 04:15
  • @Fmonkey2001: Yes, that does it. But, I don't know where I am going wrong on my thinking, why I cant get the SI by taking out 5% from the CI consecutively 2 times ? – Nikhil Sharma Nov 24 '14 at 04:23

1 Answers1

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If we knew the original debt $A$, then we could easily compute the simple interest. So let us find $A$. For simplicity let $I=252.20$.

Then the total debt after $3$ years (principal plus interest) is $A(1.05)^3$. Thus $$A+I=A(1.05)^3.$$ It follows that $A((1.05)^3-1)=I$, and therefore $$A=\frac{I}{(1.05)^3-1}.$$ Now we know $A$, and can solve the problem. Just multiply $A$ by $(3)(0.05)$.

André Nicolas
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  • Yes. that's correct. Thank you very much. Can you also try and solve the problem I had imagined to solve. Because I just wanted to know where am I going wrong and I since I need to solve this question in under 1 min so, the calculations start getting scary very soon. Thanks a lot !! – Nikhil Sharma Nov 24 '14 at 04:25
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    If you knew the total debt after $3$ years, then by dividing by $1.05$ twice, you would know the debt after $1$ year, and by dividing by $1.05$ again you would know the original debt. But we don't know the total debt after $3$ years, all we know is interest paid. – André Nicolas Nov 24 '14 at 04:37
  • I thought I if I can remove the extra 5% which would be earned in CI case only since SI would be the same for all the 3 years, I could get to SI in 1 year and then multiply the value of SI in 1 year by 3 to get my answer. Is there any way to accomplish this ? – Nikhil Sharma Nov 24 '14 at 04:41
  • What if, say I knew the answer 240. It's the SI earned for 3 years as against 252.20 earned CI in 3 years. Can I somehow manage to get 252.20 from the value of 240. Any ideas ?? – Nikhil Sharma Nov 24 '14 at 04:44
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    So unknown interest rate? We cannot. But if we know simple interest was at $5%$, we can calculate the original debt by dividing the $240$ by $3$ and then by $0.05$. After we know that, we can recover the $252.20$ in the usual way. – André Nicolas Nov 24 '14 at 05:01
  • The following might be of interest to you. If we divide the $252.20$ by $1.05$, we get a very good approximation to the simple interest. This is because $(1+r)^3-1=3r+3r^2+r^3$ ($r=0.05$), and the term $r^3$ is very small compared to $3(1+r)$. – André Nicolas Nov 24 '14 at 05:18