Question

$1,750 are deposited into an account with a 7% interest rate, compounded monthly (12 times per year). find the accumulated amount after 3 years. hint: $a = p(1 + \frac{r}{k})^{kt}$ round your answer to the nearest cent (hundredth).

Explanation:

Step1: Identify the values

We have \( P = 1750 \), \( r = 0.07 \) (since 7% = 0.07), \( k = 12 \) (compounded monthly), and \( t = 3 \) (years).

Step2: Substitute into the formula

Using the compound - interest formula \( A=P(1 + \frac{r}{k})^{kt} \), substitute the values:
\( A = 1750\times(1+\frac{0.07}{12})^{12\times3} \)

First, calculate the exponent: \( 12\times3=36 \)

Then, calculate the value inside the parentheses: \( 1+\frac{0.07}{12}=\frac{12 + 0.07}{12}=\frac{12.07}{12}\approx1.005833\)

Now, calculate \( (1.005833)^{36} \). We can use a calculator to find that \( (1.005833)^{36}\approx1.232926 \)

Finally, multiply by the principal: \( A = 1750\times1.232926\approx2157.62 \)

Answer:

\( \$2157.62 \)