Find the compound interest (CI) on ₦15,700 for 2 years at 8% per annum compounded annually.

Analysis

To find the compound interest, we first calculate the Total Amount ($A$) after 2 years using the compound interest formula, and then subtract the Principal ($P$) from that amount.

Concept

The formula for the total amount ($A$) under compound interest is:

Where:

• $P$ = Principal (₦15,700)
• $r$ = Rate (8%)
• $n$ = Time in years (2)
• Compound Interest ($CI$) = $A - P$

Step-by-Step Solution

Step 1: Identify the values

• $P = 15,700$
• $r = 8$
• $n = 2$

Step 2: Calculate the Amount ($A$)

Step 3: Calculate the Compound Interest ($CI$)

Conclusion

The compound interest on ₦15,700 for 2 years at 8% per annum is ₦2,612.48. This matches option D.

Exam Tip

When calculating compound interest for only 2 years, you can also use the "Simple Interest" method twice:

1. Find interest for Year 1: $(8\% \text{ of } 15,700) = 1,256$.
2. Add that to the principal to get the new principal for Year 2: $15,700 + 1,256 = 16,956$.
3. Find interest for Year 2: $(8\% \text{ of } 16,956) = 1,356.48$.
4. Add the two interests together: $1,256 + 1,356.48 = 2,612.48$. This is a great way to double-check your work during the exam!