Question

Alex deposits $6,000 in a Certificate of Deposit (CD) with an APR of 1.2%, compounded monthly. How much will be in the CD in 6 years, to the nearest dollar? The formula for compound interest is given below.A=P(1+r/n) ^ntAmount in 6 years: $_____

Answer 1

$

Explanation:

The formula for compound interest is given below:

`A=P\left(1+(r)/(n)\right)^(nt)\text{ where }\begin{cases}P=\text{Principal Invested} \\ r=\text{Interest Rate} \\ n=\text{Number of compounding periods}\end{cases}`

For the given problem:

• The amount Alex deposited, P = $6,000

,

• Annual Percentage Rate = 1.2% = 1.2/100 = 0.012

,

• Time, t = 6 years

,

• The number of compounding periods, n = 12 (Monthly)

Substitute these values into the formula above:

`\begin{gathered} A=6000\left(1+(0.012)/(12)\right)^(12*6) \\ =6000(1+0.001)^(72) \\ =6000(1.001)^(72) \\ =6447.70 \\ \approx\$6448 \end{gathered}`

The amount in 6 years is $6,448 (correct to the nearest dollar).