Question

If $12,000 is invested at 6% compounded quarterly, what is the amount after 6 years?The amount after 6 years will be $(Round to the nearest cent.)

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: write the given values

`\begin{gathered} P=12000 \\ R=(6)/(100)=0.06 \\ t=6\text{ years} \\ n=4\text{ since it is compounded quarterly} \end{gathered}`

STEP 2: Write the formula for Amount

`A = P(1 + (r)/(n))^(nt)`

Where:

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

STEP 3: Find the compounded amount

`\begin{gathered} A=12000(1+(0.06)/(4))^(4\cdot6) \\ A=12000(1+0.015)^(24) \\ A=12000(1.015)^(24) \\ A=12000\cdot1.429502812 \\ A=17154.03374 \\ A\approx17154.03 \end{gathered}`

Hence, the amount after 6 years will be $17154.03