alicia invested $32,000 into an account earning 3% annual interest compounded quarterly. she makes no other…

alicia invested $32,000 into an account earning 3% annual interest compounded quarterly. she makes no other deposits and does not withdraw any money. what is the balance of alicias account in 7 years? $32,426.67 $39,446.78 $43,099.36 $57,795.56

alicia invested $32,000 into an account earning 3% annual interest compounded quarterly. she makes no other deposits and does not withdraw any money. what is the balance of alicias account in 7 years? $32,426.67 $39,446.78 $43,099.36 $57,795.56

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (P) is the principal amount, (r) is the annual interest rate (in decimal form), (n) is the number of times interest is compounded per year, and (t) is the number of years. Given (P=$32000), (r = 0.03) (since (3%=0.03)), (n = 4) (compounded quarterly), and (t = 7).

Step2: Substitute the values into the formula

[ \begin{align*} A&=32000(1 +\frac{0.03}{4})^{4\times7}\ &=32000(1+0.0075)^{28}\ &=32000\times(1.0075)^{28} \end{align*} ]

Step3: Calculate ((1.0075)^{28})

Using a calculator, ((1.0075)^{28}\approx1.234243)

Step4: Calculate the value of (A)

[ \begin{align*} A&=32000\times1.234243\ &=39446.784 \end{align*} ]

Answer:

($39,446.78)