Question

A man deposited Rs.10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

Answer 1

Hint: Amount in the 15th year will be the sum of principal amount and the interest for 14 years and the amount after 20 years will be the sum of principal amount and the interest for 20 years. So we already know the principal amount is Rs. 10000. We have to find the interest using the below mentioned formula.
Simple interest can be calculated by $ \dfrac{{PTR}}{{100}} $ , where P is the principal amount, R is the interest rate and T is the time period.

Complete step-by-step answer:
The simple interest can be calculated by using the formula
 $ S.I = \dfrac{{P \times R \times T}}{{100}} $
Given that the principal amount is Rs. 10000 and the interest is 5%.
Amount in 15th year is Principal amount plus interest for 14 years.
Interest for 14 years is $ \dfrac{{PTR}}{{100}} $ , T is 14.
 $ \Rightarrow \dfrac{{10000 \times 14 \times 5}}{{100}} = Rs.7000 $
Amount in the 15th year is $ Rs.10000 + Rs.7000 = Rs.17000 $
So, the correct answer is “Rs.17000”.

Amount after 20 years is Principal amount plus interest for 20 years.
Interest for 20 years is $ \dfrac{{PTR}}{{100}} $ , T is 20.
 $ \Rightarrow \dfrac{{10000 \times 20 \times 5}}{{100}} = Rs.10000 $
Amount after 20 years is $ Rs.10000 + Rs.10000 = Rs.20000 $
Therefore, the amount in the 15th year is Rs.17000 and the amount after 20 years is Rs.20000
So, the correct answer is “Rs.20000”.

Note: Another approach.
Interest per year is 5%, this means $ 10000 \times \dfrac{5}{{100}} = Rs.500 $
Amount in 1st year is 10,000; amount in 2nd year is 10,500; amount in 3rd year is 11,000.
Then the amounts in all the years will be in an A.P. with 10000 as the first term ‘a’ and 500 as common difference ‘d’.
General form of a term in an A.P is $ a + \left( {n - 1} \right)d $
So for the amount in 15th year, n will be 15.
This means the amount will
 $ \Rightarrow 10000 + \left( {15 - 1} \right)500 = 10000 + \left( {14 \times 500} \right) = 10000 + 7000 = Rs.17000 $ . In the same way, the amount after 20 years will be the amount in the 21st year, which means n is 21.Amount in 21st year will be
 $ \Rightarrow 10000 + \left( {21 - 1} \right)500 = 10000 + \left( {20 \times 500} \right) = 10000 + 10000 = Rs.20000 $