2. john wants to have $15,000 in 5 years after investing in an account that earns 5.25% compounded monthly…

Explanation:

Step1: <Formula for compound interest>

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (A) is the final amount ((A = 15000)), (P) is the principal amount (initial investment, which we want to find), (r) is the annual interest rate (as a decimal, (r=0.0525)), (n) is the number of times interest is compounded per year ((n = 12) for monthly compounding), and (t) is the number of years ((t = 5)).

We need to solve the formula for (P). Rearranging the formula gives (P=\frac{A}{(1 +\frac{r}{n})^{nt}}).

Step2: <Substitute the values into the formula>

Substitute (A = 15000), (r=0.0525), (n = 12), and (t = 5) into the formula:

First, calculate (\frac{r}{n}=\frac{0.0525}{12}=0.004375) and (nt=12\times5 = 60).

Then ((1+\frac{r}{n})^{nt}=(1 + 0.004375)^{60}).

Using a calculator, ((1+0.004375)^{60}\approx1.2939).

Step3: <Calculate the value of (P)>

(P=\frac{15000}{1.2939}\approx11592.7)

Answer:

(P\approx$11592.7)