Question

What sum of money invested at 12% simple interest will secure the same income as Rs. 25,000
can secure at 18% (simple interest).

Answer 1

To find the sum of money that needs to be invested at 12% simple interest to secure the same income as Rs. 25,000 invested at 18% simple interest, we can start by calculating the income from Rs. 25,000 at 18%.

The formula for simple interest (SI) is:

\[
SI = \frac{P \times R \times T}{100}
\]

where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

Assuming we want to find the income for a period of 1 year, let’s calculate the income from Rs. 25,000 at 18% for 1 year.

\[
SI = \frac{25000 \times 18 \times 1}{100} = \frac{25000 \times 18}{100} = 4500
\]

So, Rs. 25,000 at 18% generates an income of Rs. 4,500 in 1 year.

Next, let’s denote the principal amount we need to invest at 12% as \(P\). We want this investment also to yield Rs. 4,500 in interest over 1 year.

Using the simple interest formula again for the investment at 12%:

\[
4500 = \frac{P \times 12 \times 1}{100}
\]

Now, we can solve for \(P\):

\[
4500 = \frac{P \times 12}{100}
\]

Multiplying both sides by 100 to eliminate the fraction:

\[
4500 \times 100 = P \times 12
\]

\[
450000 = P \times 12
\]

Now, divide both sides by 12 to solve for \(P\):

\[
P = \frac{450000}{12} = 37500
\]

Thus, the sum of money that needs to be invested at 12% simple interest to secure the same income as Rs. 25,000 at 18% is **Rs. 37,500**.