b) Find the amount of ₵400,000 at 7% capitalized semiannually in 7 years.

Given:

P = ₵400000

Annual interest rate of 7%, compounded semiannually: r = 0.07 and n = 2

Time period = 7 years: t = 7

Step 1: Identify the formula A = P \left(1 + \frac{r}{n}\right)^{nt}

Step 2: Substitute the known values into the formula:

A = 400000 \left(1 + \frac{0.07}{2}\right)^{2 \cdot 7}

Step 3: Simplify inside the parentheses:

A = 400000 \left(1 + 0.035\right)^{14}

A = 400000 \left(1.035\right)^{14}

A\approx647477.81

Therefore, the final amount is:

A\approx647477.81