Question

Clearly your work by step by step answer the question below.
If k15 000 000 is deposited in an account and after 5 years the balance becomes K25 000 000.
Calculate the compound interest rate applied

Answer 1

To find the compound interest rate applied, we can use the formula for compound interest:

\[
A = P(1 + r)^n
\]

where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in decimal).
- \( n \) is the number of years the money is invested or borrowed.

### Step 1: Identify the variables

- \( A = K25,000,000 \) (the final amount)
- \( P = K15,000,000 \) (the principal)
- \( n = 5 \) years (the time period)
- \( r = ? \) (the interest rate we want to find)

### Step 2: Plug in the values into the formula

\[
25,000,000 = 15,000,000(1 + r)^5
\]

### Step 3: Divide both sides by 15,000,000 to isolate the compound interest factor

\[
\frac{25,000,000}{15,000,000} = (1 + r)^5
\]

Calculating the left side:

\[
\frac{25,000,000}{15,000,000} = \frac{25}{15} = \frac{5}{3} \approx 1.6667
\]

So the equation becomes:

\[
1.6667 = (1 + r)^5
\]

### Step 4: Take the fifth root of both sides to solve for \( 1 + r \)

\[
1 + r = (1.6667)^{\frac{1}{5}}
\]

### Step 5: Calculate \( (1.6667)^{\frac{1}{5}} \)

Using a calculator:

\[
1 + r \approx 1.1146
\]

### Step 6: Solve for \( r \)

\[
r \approx 1.1146 - 1 = 0.1146
\]

### Step 7: Convert \( r \) to a percentage

\[
r \approx 0.1146 \times 100 \approx 11.46\%
\]

### Conclusion

The compound interest rate applied is approximately **11.46%** per year.