Solution:

Here,

For the first year:

Principal (P1) = Rs. 55,000

Rate of interest (R1) = 10% p.a.

Time (T1) = 1 year

Annual compound interest (CI1) =?

By formula,

CI1 = \(p1\left\{\left(1+\frac{R1}{100}\right)^{T1}-1\right\}\)

= \(55000\left\{\left(1+\frac{10}{100}\right)^1-1\right\}\)

= \(55000\left\{\left(1.1\right)-1\right\}\)

= Rs. 5500

∴ Compound interest of the first year (CI1) = Rs. 5500

And, compound Amount after 1 year (CA1) = P1 + CI1 = Rs. 60,500

Again,

For the second year:

Principal (P2) = CA1 = Rs. 60,500

Rate of interest (R2) = 10% p.a.

Time (T2) = 1 year

Semi-annual interest (CI2) = ?

By formula,

Semi-annual compound interest (CI2)

= \(P2\left\{\left(1+\frac{R2}{200}\right)^{2\cdot T2}-1\right\}\)

= \(60500\left\{\left(1+\frac{10}{200}\right)^2-1\right\}\)

= \(60500\left\{1.1025-1\right\}\)

= \(\left\{60500\cdot0.1025\right\}\)

= Rs. 6201.25

Here, CI2 - CI1 = Rs. 6201.25 - Rs. 5500

= Rs. 701.25

∴ The interest of the second year is more than the interest of the first year by Rs. 701.25

Now, the difference in interest in percentage = \( \frac{diffininterest}{CI1}\cdot100\%\)

= \(\frac{Rs701.25}{Rs5500}\cdot100\%\)

= 12.75%

**∴ The interest of the second year is 12.7% more than the interest of the second year.**

**The general formula for compound interest.**

The formula for compound interest is:

**A = P(1 + r/n)^(nt)**

Where:

A = the future value of the investment/loan, including interest

P = the principal amount (the initial investment/loan amount)

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is invested/borrowed for

This formula calculates the amount of interest earned on an investment or the amount of interest owed on a loan, taking into account the compounding effect of earning interest on both the principal amount and any previously earned interest. The more frequently the interest is compounded, the greater the impact on the overall amount of interest earned.