The interest on a certain deposit at 4.5% p.a. is Rs. 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a.?

1. Break Down the Problem

To find the additional interest for one year at 5% p.a. compared to 4.5% p.a., we need to:

1. Determine the principal amount based on the interest earned at 4.5%.
2. Calculate the interest at 5% on the same principal.
3. Find the difference between the two interest amounts.

2. Relevant Concepts

• Formula for calculating interest: $\text{Interest} = \text{Principal} \times \frac{\text{Rate}}{100} \times \text{Time}$

3. Analysis and Detail

1. Calculate Principal from 4.5% Interest:

   • Given interest $I = 202.50$ and rate $r = 4.5 \%$: $202.50 = \text{Principal} \times \frac{4.5}{100} \times 1$
   • Rearranging to find the principal: $\text{Principal} = \frac{202.50 \times 100}{4.5} = 4500$

2. Calculate Interest at 5%:

   • Use the principal identified above: $I_{5\%} = 4500 \times \frac{5}{100} \times 1 = 225$

3. Calculate Additional Interest:

   • Additional interest at 5% compared to 4.5%: $\text{Additional Interest} = I_{5\%} - I_{4.5\%} = 225 - 202.50 = 22.50$

4. Verify and Summarize

• The principal is calculated correctly as Rs. 4500.
• The 5% interest on this principal is Rs. 225.
• The additional interest earned when switching from 4.5% to 5% is Rs. 22.50.

Final Answer

The additional interest in one year at 5% p.a. will be Rs. 22.50.