A sum is being lent at `20%` p.a. compound interest. What is the ratio of increase in amount of `4^(th)` year to.`5^(th)` year?

Options

A. 0.17013888888889
B. `5:4`
C. `5:6`
D. can't be determined

Explanation

To find the ratio of the increase in amount from the 4th year to the 5th year at a compound interest rate of 20% per annum, we will follow these steps:

### Step 1: Understand the Concept of Compound Interest
In compound interest, the interest for each year is calculated on the total amount accumulated until that year, which includes the principal and the interest from previous years.

### Step 2: Calculate the Amount at the End of Each Year
Assuming the principal amount is \( P \), the amount at the end of each year can be calculated using the formula:
\[
...