JAMB 2015 Mathematics · Question 46

The amount A to which a principal P amounts at r% compound interest for n years is given by the formula A =…

Question

The amount A to which a principal P amounts at r% compound interest for n years is given by the formula A = P(1 + (r ÷ 100) $^n$ . Find A, if P = 126, r = 4 and n = 2.

A.N132.50K
B.N136.30K
C.N125.40K
D.N257.42K

Answer: B. N136.30K

Explanation written with AI and checked against the answer key

Analysis

The question asks us to calculate the final amount ( $A$ ) using the compound interest formula. We are given the principal ( $P$ ), the rate ( $r$ ), and the time period ( $n$ ).

Concept

The formula for compound interest is:

A = P\left(1 + \frac{r}{100}\right)^n

Where:

$P$ = Principal (the initial amount)
$r$ = Interest rate per annum
$n$ = Number of years

Step-by-Step Solution

Step 1: Identify the given values

$P = 126$
$r = 4$
$n = 2$

Step 2: Substitute the values into the formula

A = 126 \left(1 + \frac{4}{100}\right)^2

Step 3: Simplify the expression inside the bracket

\frac{4}{100} = 0.04

A = 126(1 + 0.04)^2

A = 126(1.04)^2

Step 4: Calculate the square of 1.04

1.04 \times 1.04 = 1.0816

Step 5: Multiply by the principal

A = 126 \times 1.0816

A = 136.2816

Rounding this to two decimal places (as is standard for currency in Naira and Kobo), we get N136.28.

Evaluation of Options

The calculated value is approximately N136.28. Looking at the provided options: A. N132.50 B. N136.30 C. N125.40 D. N257.42

While our precise calculation is 136.28, option B is the closest approximation to the result.

Exam Tip

When dealing with compound interest questions in JAMB, always calculate the decimal value carefully. If your answer is very close to one of the options (like 136.28 vs 136.30), it is likely due to rounding differences in the exam board's calculation process. Always choose the option that is closest to your result.

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