Question

Question 1336 ptsUse the compound interest formulas A=1+ntand A = Per to solve.Find the accumulated value of an investment of $10,000 at 4% compoundedsemiannually for 5 years.O $11,040.81O $12,000.00$12,189.94O $12,166.53

Answer 1

Step 1: We shall state the Compound Interest formula.

$A=P(1+\frac{r}{100\alpha})^{n\alpha}$$\begin{gathered} \text{Where A = amount =?} \\ P=Pr\text{incipal =\ 10,000} \\ r=\text{rate = 4\%} \\ n\text{ = number of years = 5 years} \\ \alpha\text{ =number of periods per year = 2 (Since, it is semi-annually)} \end{gathered}$

Step 2: we shall substitute the values of the parameters in the formula.

$A=10000(1+\frac{4}{100\times2})^{5\times2}$$\begin{gathered} A=10000(1+\frac{4}{200})^{10} \\ A=10000(1+0.02)^{10} \\ A=10000(1.02)^{10} \\ A=10000(1.21899) \\ A=12,189.944\approx\text{ \ 12,189.94} \end{gathered}$

Thus, the correct answer is $12,189.94 (option