Question

how to calculate the amount compounded to 6 years not only one year1) $3000 deposit that earns 6% annual interest compounded quarterly for 6 years

Answer 1

Step 1

State the compound interest formula

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

Where;

`\begin{gathered} A=\text{ amount} \\ P=Prin\text{cipal}=\text{\$3000} \\ r=\text{ rate= }\frac{\text{6}}{100}=0.06 \\ n=\text{ number of periods of compounding= 4} \\ t=\text{ time = 6 years} \end{gathered}`

Step 2

Find the amount as required

`\begin{gathered} A=3000(1+(0.06)/(4))^(6*4) \\ A=3000(1+0.015)^(24) \\ A=3000(1.015)^(24) \\ A=\text{\$}4288.508436 \\ A\approx\text{ \$}4288.51 \end{gathered}`

Hence the amount compounded quarterly for 6 years based on a principal of $3000 and a 6% annual interest rate = $4288.51