Question

Suppose that you put $1,500 into a certificate of deposit that pays 2% per year,

compounded monthly. If you leave the money in that account for 5 years, how
much will this CD be worth when you withdraw your funds?

$1,604.69
$18,150.50
$1,657.62
$19,873.45

Answer 1

To find the value of a $1,500 CD with 2% interest, compounded monthly after 5 years, we use the compound interest formula. The correct value is $1,657.62.

Step-by-step explanation:

To calculate the value of a $1,500 certificate of deposit (CD) that pays 2% interest per year, compounded monthly, over a period of 5 years, we use the compound interest formula:

A = P(1 + r/n)nt

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

In this case:

P = $1,500

r = 0.02 (2% expressed as a decimal)

n = 12 (since the interest is compounded monthly)

t = 5

Plugging these values into the formula gives us:

A = $1,500(1 + 0.02/12)12*5

After calculating, the value of the CD at the end of the 5 years is $1,657.62.

Answer 2

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1500\\ r=rate\to 2\%\to (2)/(100)\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}`

`A=1500\left(1+(0.02)/(12)\right)^(12\cdot 5)\implies A=1500\left( (601)/(600) \right)^(60)\implies A\approx 1657.62`