Question : If the amount on a certain principal in 3 years at a 12% rate of interest compounded annually is Rs. 12,000, what will be the amount (in Rs.) after the 4th year?
Option 1: 14,330
Option 2: 15,440
Option 3: 13,440
Option 4: 14,550
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Correct Answer: 13,440
Solution : We have, $A = 12000, r = 12\%, n = 1 $ (compounded annually) and $t = 3$ years. $A = P \left(1+\frac{r}{100}\right)^{t}$ Substituting the given values into the formula, $⇒12000 = P (1+\frac{12}{100})^{1×3}$ $⇒12000 = P (1.12)^{3}$---(i) For $t = 4$ year $⇒ A = P(1 + \frac{12}{100})^{4}$ $⇒ A = P (1.12 )^{4}$---(ii) Divide equation (ii) by (i), we get $⇒A = 12000×1.12 = 13440$ Hence, the correct answer is Rs. $13440$.
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