To solve this problem, follow these steps to find the compound interest on N2650 in 5 years at a 7% annual interest rate:
1. Identify the given values:
- Principal (P) = N2650
- Annual interest rate (r) = 7% or 0.07 (as a decimal)
- Time (t) = 5 years
- The interest is compounded annually, so the number of times interest is compounded per year (n) = 1
2. Use the compound interest formula:
[tex]\[
A = P\left(1 + \frac{r}{n}\right)^{nt}
\][/tex]
where:
- [tex]\(A\)[/tex] is the amount after the interest is added.
- [tex]\(P\)[/tex] is the principal amount (initial investment).
- [tex]\(r\)[/tex] is the annual interest rate (in decimal form).
- [tex]\(n\)[/tex] is the number of times the interest is compounded per year.
- [tex]\(t\)[/tex] is the time the money is invested for in years.
3. Plug in the given values:
[tex]\[
A = 2650 \left(1 + \frac{0.07}{1}\right)^{1 \times 5}
\][/tex]
4. Solve inside the parentheses first:
[tex]\[
A = 2650 \left(1 + 0.07\right)^5
\][/tex]
[tex]\[
A = 2650 \left(1.07\right)^5
\][/tex]
5. Calculate [tex]\( (1.07)^5 \)[/tex]:
[tex]\( (1.07)^5 = 1.402552 \)[/tex] (approximately)
6. Multiply by the principal amount (P):
[tex]\[
A = 2650 \times 1.402552 \approx 3716.76
\][/tex]
7. Calculate the compound interest:
[tex]\[
\text{Compound interest} = A - P
\][/tex]
[tex]\[
\text{Compound interest} = 3716.76 - 2650
\][/tex]
[tex]\[
\text{Compound interest} = 1066.76
\][/tex]
The compound interest on N2650 in 5 years at 7% per annum is approximately N1066.76.
Comparing this with the given options, none exactly match the calculated value. However, this is indeed the correct detailed calculation.
