Question

exponential models
guided practice
encouraged by his investment, joseph decides to open another cd account. this time, he deposits $1,000 and plans to leave it untouched for 3 years. in exchange, the bank will pay him 0.3% interest every month. how much will be in the account when the 3 years have passed?
a. $1,036.60
b. $1,009.03
c. $12,646,218.55
d. $1,113.87

Explanation:

Step1: Identify the formula for compound interest

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, 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.

Step2: Extract the values from the problem

• $P = \$1000$ (the principal amount)
• $r = 0.3\%$ per month. First, convert the monthly rate to an annual rate. Since there are 12 months in a year, the annual rate $r = 0.3\% \times 12 = 3.6\% = 0.036$ (in decimal form).
• $n = 12$ (compounded monthly, so 12 times per year)
• $t = 3$ years (the time the money is invested)

Step3: Substitute the values into the formula

Substitute $P = 1000$, $r = 0.036$, $n = 12$, and $t = 3$ into the compound - interest formula:

$$
LATEXBLOCK0
$$

Step4: Calculate $(1.003)^{36}$

Using a calculator, $(1.003)^{36}\approx1.11387$

Step5: Calculate the final amount $A$

Multiply the principal by the calculated factor:
$A = 1000\times1.11387=\$1113.87$

Answer:

D. $1,113.87$