Question

Ram borrows $₹22500$ at $10\%$ per annum, compounded annually. If he repays $₹11250$ at the end of first year and $₹12550$ at the end of the second year, find the amount of loan outstanding against him at the end of third year.

Answer 1

Given that

Principal (P) $=$ $₹22500$
Rate (R) $=10\%p.a.$
Time (T) $=3years$

We need to find the amount of loan outstanding against him at the end of the third year

We know that if money borrowed on compound interest then

$Amount=P{(1+\frac{R}{100})}^T$

Let us calculate the amount yearly

Step 1

Beginning with the first year:
Amount at the end of the first year $=P{(1+\frac{R}{100})}^1=22500{(1+\frac{10}{100})}^1=22500x\frac{11}{10}=₹24750$
Amount paid at the end of the first year $=₹11250$(given)
Balance after the first year $=₹24750–₹11250=₹13500$

Now, this balance becomes principal for next year's calculation.

Amount at the end of 2nd year $=₹13500{(1+\frac{10}{100})}^1=₹13500x\frac{11}{10}=₹14850$
Amount paid at the end of the second year $=₹12550$(given)
Balance after the second year $=₹14850-₹12550=₹2300$

Now, this balance becomes principal for next year's calculation.

Amount at the end of the third year $=2300{(1+\frac{10}{100})}^1=2300x\frac{11}{10}=₹2530$

Hence the amount of loan outstanding against him at the end of the third year is $₹2530$