a couple deposits $18,000 into an account earning 2% annual interest for 15 years. calculate the future…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is (A = P\left(1+\frac{r}{n}\right)^{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 that (P=$18000), (r = 2%=0.02), (n = 4) (compounded quarterly), and (t = 15) years.

Step2: Substitute the values into the formula

First, calculate the exponent (nt): (nt=4\times15 = 60)

Then, calculate the value of (\left(1+\frac{r}{n}\right)): (\frac{r}{n}=\frac{0.02}{4}=0.005), and (1+\frac{r}{n}=1 + 0.005=1.005)

Now, substitute into the formula: (A=18000\times(1.005)^{60})

Step3: Calculate ((1.005)^{60})

Using a calculator, ((1.005)^{60}\approx1.3488501525)

Step4: Calculate (A)

(A = 18000\times1.3488501525\approx24279.30)

Answer:

(24279.30)