Question

you plan to deposit $78,750 into a savings account that has a 6.09% interest rate compounded quarterly. what will be the balance of your savings account after 6 years? use this formula: $a = p(1 + \frac{r}{n})^{nt}$ enter the dollar amount rounded to the nearest cent. your answer: answer

Explanation:

Step1: Identify the values

Here, \( P = 78750 \) (principal amount), \( r = 6.09\% = 0.0609 \) (annual interest rate), \( n = 4 \) (compounded quarterly), and \( t = 6 \) (number of years).

Step2: Substitute into the formula

Substitute the values into the compound - interest formula \( A = P(1+\frac{r}{n})^{nt} \).
First, calculate \( \frac{r}{n}=\frac{0.0609}{4}=0.015225 \).
Then, calculate \( nt = 4\times6 = 24 \).
Next, calculate \( 1+\frac{r}{n}=1 + 0.015225=1.015225 \).
Then, raise this value to the power of \( nt \): \( (1.015225)^{24} \). Using a calculator, \( (1.015225)^{24}\approx1.433447 \).
Finally, calculate \( A=78750\times1.433447\approx112983.95 \).

Answer:

\( \$112983.95 \)