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On what sum of money will the C.I. of 2 yrs be the same as the S.I. on Rs. 412 for 10 yrs, the rate of interest being 6% per annum?
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On what sum of money will the C.I. of 2 yrs be the same as the S.I. on Rs. 412 for 10 yrs, the rate of interest being 6% per annum?
1). Rs. 2200
2). Rs. 24000
3). Rs. 2000
4). Rs. 1600
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Formulas to be used:-
SI, I = ( P × r × t ) / 100
For CI:
$(A\; = \;P\;{\left( {\;1\; + \frac{r}{{100}}\;} \right)^t})$; CI = A – P
Where SI is Simple interest,
A is the amount at the end of time t,
P is the principal,
t is time,
r is rate
Given, CI on a certain sum for 2 years at 6% per annum.
$(A = P{\left( {\;1 + \frac{6}{{100}}} \right)^2})$
⇒ A = P(1.06)2
⇒ A = 1.1236P
∴ CI = A – P
⇒ CI = 1.1236P – P
⇒ CI = 0.1236P
SI on Rs. 412 for 10 years at 6% per annum
$(\Rightarrow SI = \frac{{412 \times 10 \times 6}}{{100}})$
⇒ SI = Rs. 247.20
Given, C.I. of 2 yrs be the same as the S.I. on Rs. 412 for 10 yrs
∴ 0.1236P = 247.20
⇒ P = Rs. 2000