Sure! Let's approach this step by step using the compound interest formula:
The formula for compound interest is:
\(\[ A = P (1 + \frac{r}{n})^{nt} \]\)
where:
- \(\( P \)\) is the principal amount (9600 in this case)
- \(\( r \)\) is the annual interest rate (expressed as a decimal, so 10% becomes 0.10)
- \(\( n \)\) is the number of times the interest is compounded per year (since it's compounded annually in this case, \(\( n = 1 \)\))
- \(\( t \)\) is the number of years the money is invested (3 years)
However, since we're calculating per annum (annually), we can simplify the formula to:
\(\[ A = P (1 + r)^t \]\)
Let's calculate each part of the question:
### (i) The sum due at the end of the first year:
Given:
- \(\( P = 9600 \)\)
- \(\( r = 0.10 \)\)
- \(\( t = 1 \)\) (since we are interested in the first year)
Using the formula:
\(\[ A_1 = 9600 \times (1 + 0.10)^1 \]\)
\(\[ A_1 = 9600 \times 1.10 \]\)
\(\[ A_1 = 10560 \]\)
So, the sum due at the end of the first year is ₦10,560.
### (ii) The sum due at the end of the second year:
Given:
- \(\( P = 9600 \)\)
- \(\( r = 0.10 \)\)
- \(\( t = 2 \)\) (for the end of the second year)
Using the formula:
\(\[ A_2 = 9600 \times (1 + 0.10)^2 \]\)
\(\[ A_2 = 9600 \times (1.10)^2 \]\)
\(\[ A_2 = 9600 \times 1.21 \]\)
\(\[ A_2 = 11616 \]\)
So, the sum due at the end of the second year is ₦11,616.
### (iii) The compound interest earned in the first 2 years:
Compound interest earned is the amount accumulated minus the principal.
For the end of two years:
- The amount accumulated at the end of two years is ₦11,616.
- The principal is ₦9600.
Thus, the compound interest earned in the first two years is:
\(\[ \text{Compound Interest} = A_2 - P \]\)
\(\[ \text{Compound Interest} = 11616 - 9600 \]\)
\(\[ \text{Compound Interest} = 2016 \]\)
So, the compound interest earned in the first 2 years is ₦2,016.
In summary:
1. The sum due at the end of the first year is ₦10,560.
2. The sum due at the end of the second year is ₦11,616.
3. The compound interest earned in the first 2 years is ₦2,016.
