Question

A sum of money invested at 6% p.a simple interest for a certain period of time yields Rs 960 as interest. If this sum had been invested for 5 years more, it would have yielded Rs 2160 as interest. Find the sum.

Answer 1

Hint: Here we are given simple interest after two time periods and we have to calculate the principal value or we can say sum of money deposited. We will use a simple interest formula to form two equations and solve them to find the value of simple interest. Formula for finding simple interest is given by
\[SI=\dfrac{P\times R\times T}{100}\]
Where P is the principal amount or sum, R is the rate of interest per annum and T is the time period.

Complete step by step answer:
We are given that the sum of money is invested at 6%. Therefore,
\[R=6\]
We have to find the principal amount or sum. Hence, we can suppose sum as P.
We are also not given an exact time period. So, let us suppose Tis the time period when Rs 960 was the simple interest calculated.
Simple Interest is given by:
\[SI=\dfrac{P\times R\times T}{100}\]………equation (1)
Where P is principal amount or sum, R is rate of interest and T is time period. We are also given simple interest after T years to be Rs 960, putting all values in above equation, we get
\[960=\dfrac{P\times 6\times T}{100}\]
Cross multiply,
\[P\times T\times 6=960\times 100\]
\[P\times T=16000\]……………. equation (2)
Now, after 5 more years, the time period will become \[(T+5)\]years. Rate of interest remains the same. Principal amount will also remain the same. Hence, putting them again in equation (1), we get
How, simple interest becomes Rs2160
\[SI=\dfrac{P\times 6\times (T+5)}{100}\]
\[2160=\dfrac{6\times P\times (T+5)}{100}\]
Cross multiplying,
\[2160\text{ }\times \text{ }100\text{ = }6\times P\times T+30\times P\text{ }\]
\[6\times P\times T+30\times P\text{ = }2160\text{ }\times \,\,100\]
Putting value of \[P \times T\] from equation (2), we get
\[6 \times 16000+30\times P\text{ = }216000\]
\[30\times P\text{ = 12}0000\]
\[P\text{ = Rs 4}000\]

Hence, principal amount or we can say sum is Rs 4000.

Note: Students should take care that we are given 5 more years and not just 5 years. They should not make the mistake of putting 5 in value of T instead of \[(T+5)\]. Also 100 is already divided in formula, so rate of interest should be numerical value only. Students should learn these formulas as these are important for these types of questions.