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A sum of money invested at compound interest amount to Rs. 4624 in 2 years and to Rs. 4913 in 3 years. The sum of money is:
1. Rs. 4096
2. Rs. 4260
3. Rs. 4335
4. Rs. 4360

1 Answer

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Best answer
Correct Answer - Option 1 : Rs. 4096

Given:

Amount in second year = 4624 Rs.

Amount in Third year = 4913 Rs.

Formula used 

\(Amount = P\;{\left( {1 + \frac{r}{{100}}} \right)^t}\)

Where P is the principal, r is the rate of interest and t be the time

Solution:

Accordingly,

\(4624 = \;{P\left( {1 + \frac{r}{{100}}} \right)^2}\)      ----(i)

\(4913 = P\;{\left( {1 + \frac{r}{{100}}} \right)^3}\)      ----(ii)

Divide eq (ii) by (i)

\(\frac{{4913}}{{4624}} = {\left( {1 + \frac{r}{{100}}} \right)^1}\)      ----(iii)

\(r = \frac{{\left( {4913 - 4624} \right) × 100}}{{4624}} \)

r = 6.25%

6.25% = 1/16

from Eq (i) 

4624 = P× (17/16)× (17/16)

⇒ P = 4096

∴ The sum of money is Rs. 4096

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