If $32,500 is invested at 69% for 3 years find the future value if the interest is compounded the following ways.

annually, semiannually, quarterly, monthly, daily, every minute (N-525,600)
continuously, simple (not compounded.

Thank you for your time.

Po = $32,500 @ 69%? for 3 years.

P1 = Po(1+r)^n. Compounded annually.
P1 = 32,500(1+0.69)^3 = $156,871.29

P2 = 32,500(1+0.69/2)^6 = 192,405.32

P3 = 32,500(1+0.69/4)^12 = 219,400.48

P4 = 32,500(1+0.69/12)^36 = 243,207.46

P5 = 32,500(1+0.69/365)^1095=257,053.95

P6 = 32,500(1+0.69/525,600)^1,576,800 =
257,556.40

P7 = Po*e^(r*t) = 32,500*e^(0.69*3) =
257,556.75

P8 = Po + Po*r*t=32000 + 32,500*0.69*3 = 98,240. Simple Int.

To find the future value of an investment with compound interest, we can use the formula:

\[A = P\left(1 + \frac{r}{n}\right)^{nt}\]

Where:
A = Future Value
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

Given:
P = $32,500
r = 69% = 0.69 (as a decimal)
t = 3 years
N = 525,600 (number of minutes in a year, assuming 365 days)

Now, let's calculate the future value for each compounding period:

1. Annually (n = 1):
\[A = 32,500\left(1 + \frac{0.69}{1}\right)^{1 \cdot 3}\]
Solving this equation will give you the future value when compounded annually.

2. Semiannually (n = 2):
\[A = 32,500\left(1 + \frac{0.69}{2}\right)^{2 \cdot 3}\]
Solving this equation will give you the future value when compounded semiannually.

3. Quarterly (n = 4):
\[A = 32,500\left(1 + \frac{0.69}{4}\right)^{4 \cdot 3}\]
Solving this equation will give you the future value when compounded quarterly.

4. Monthly (n = 12):
\[A = 32,500\left(1 + \frac{0.69}{12}\right)^{12 \cdot 3}\]
Solving this equation will give you the future value when compounded monthly.

5. Daily (n = 365):
\[A = 32,500\left(1 + \frac{0.69}{365}\right)^{365 \cdot 3}\]
Solving this equation will give you the future value when compounded daily.

6. Every minute (n = 525,600):
\[A = 32,500\left(1 + \frac{0.69}{525,600}\right)^{525,600 \cdot 3}\]
Solving this equation will give you the future value when compounded every minute.

7. Continuously:
\[A = 32,500e^{0.69 \cdot 3}\]
Solving this equation will give you the future value when compounded continuously.

8. Simple Interest:
\[A = 32,500 + (32,500 \cdot 0.69 \cdot 3)\]
Solving this equation will give you the future value with simple interest.

By calculating these equations, you can find the future value for each compounding period.