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If the compound interest on a sum for 2 years at 12.5% p.a. is rs. 510, the simple interest on the same sum at the same rate for the same period of time is
- ARs. 400
- BRs. 450
- CRs. 460
- DRs. 480
Answer not set
Discussion 1
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CCommunity
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 on CI at the end of time t,
P is the principal,
t is time,
r is rate
Given, compound interest on a sum for 2 years at 12.5 p.a. is rs. 510.
$(A = P\;{\left( {\;1 + \frac{{12.5}}{{100}}} \right)^2})$
⇒ A = P(1.125)2
⇒ A = 1.265625P
CI = A – P
⇒ CI = 1.265625P – P
⇒ CI = 0.265625P
Given, CI = Rs. 510
∴ 0.265625P = 510
⇒ P = Rs. 1920
SI on the same sum at the same rate for the same period of time is:
SI = (1920 × 12.5 × 2)/100
⇒ SI = Rs. 480
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 on CI at the end of time t,
P is the principal,
t is time,
r is rate
Given, compound interest on a sum for 2 years at 12.5 p.a. is rs. 510.
$(A = P\;{\left( {\;1 + \frac{{12.5}}{{100}}} \right)^2})$
⇒ A = P(1.125)2
⇒ A = 1.265625P
CI = A – P
⇒ CI = 1.265625P – P
⇒ CI = 0.265625P
Given, CI = Rs. 510
∴ 0.265625P = 510
⇒ P = Rs. 1920
SI on the same sum at the same rate for the same period of time is:
SI = (1920 × 12.5 × 2)/100
⇒ SI = Rs. 480