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+(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+(4)/(100*2))^(5*2)`
`\begin{gathered} A=10000(1+(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