Question

200 is invested at 4% per year compounded semi - annually. the amount obtained after 5 years is
a) $240.00
b) $243.80
c) $243.33
d) $244.04

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $P=\$200$, $r = 0.04$ (since $4\%=0.04$), $n = 2$ (semi - annual compounding), and $t = 5$ years.

Step3: Substitute values into the formula

$A=200(1 +\frac{0.04}{2})^{2\times5}=200(1 + 0.02)^{10}$.

Step4: Calculate the value inside the parentheses

$(1 + 0.02)^{10}=1.02^{10}$. Using a calculator, $1.02^{10}\approx1.21899442$.

Step5: Calculate the final amount

$A = 200\times1.21899442=\$243.80$.

Answer:

b) $\$243.80$