Question : A loan of Rs. 12300 at 5% per annum Compound Interest be repaid in two equal annual instalments at the end of every year. Find the amount of each instalment.
Option 1: Rs. 6651
Option 2: Rs. 6615
Option 3: Rs. 6516
Option 4: Rs. 6156
Correct Answer: Rs. 6615
Solution :
Let the instalment value be Rs. $P$.
According to the concept,
$\frac{x}{(1+\frac{R}{100})} +\frac{x}{(1+\frac{R}{100})^2} +...........+\frac{x}{(1+\frac{R}{100})^n} =A$
where $x$ is the instalment value, 'A' is the total amount that was created in instalments and n is the number of instalments.
$P(1+\frac{5}{100})+P=12300(1+\frac{5}{100})^{2}$
⇒ $1.05P+P=12300×\frac{21}{20}×\frac{21}{20}$
⇒ $2.05P=13560.75$
⇒ $P=\frac{13560.75}{2.05}$ = 6615
Hence, the correct answer is Rs. 6615.
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