Let's break down each question step by step.

Question 2: Future Value of a Lump Sum Investment

You won $3,000 and plan to invest it at an annual interest rate of 8% compounded monthly. To calculate the future value (FV) after 10 years, we can use the formula:

$FV = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $P$ = principal amount ($3,000)
• $r$ = annual interest rate (0.08)
• $n$ = number of times interest is compounded per year (12 for monthly)
• $t$ = number of years (10)

Plugging in the values:

$FV = 3000 \left(1 + \frac{0.08}{12}\right)^{12 \times 10}$

Calculating this:

1. Calculate $\frac{0.08}{12} = 0.00666667$.
2. Calculate $1 + 0.00666667 = 1.00666667$.
3. Calculate $12 \times 10 = 120$.
4. Raise $1.00666667$ to the power of $120$.
5. Multiply by $3,000.

$FV \approx 3000 \times 2.21964 \approx 6658.92$

The closest option is $6,658.92.

Question 3: Present Value of an Annuity

Jennifer's treadmill payments of $100 per month for 4 years at an annual interest rate of 17% compounded monthly can be calculated using the present value of an annuity formula:

$PV = PMT \times \left(\frac{1 - (1 + r/n)^{-nt}}{r/n}\right)$

Where:

• $PMT$ = monthly payment ($100)
• $r$ = annual interest rate (0.17)
• $n$ = number of payments per year (12)
• $t$ = number of years (4)

Plugging in the values:

1. Calculate $\frac{0.17}{12} \approx 0.01416667$.
2. Calculate $n \times t = 12 \times 4 = 48$.
3. Calculate $PV = 100 \times \left(\frac{1 - (1 + 0.01416667)^{-48}}{0.01416667}\right)$.

Calculating this gives:

$PV \approx 100 \times 3.992 \approx 399.20$

You will find that $PV$ yields values close to the options.

Question 4: Loan Payment Type

The problem describes a loan to pay off in monthly installments, which indicates it is an Amortization problem. The monthly payments are calculated to pay off the loan amount over a fixed term with interest.

Summary of Answers

1. Question 2: $6,658.92
2. Question 3: Calculating the exact value needed, but likely close to one of the options.
3. Question 4: Amortization

Do you want detailed calculations for Question 3 or have any questions? Here are some follow-up questions:

1. Would you like to see the detailed calculation steps for the treadmill question?
2. How does compounding frequency affect the future value of investments?
3. What are the implications of a higher interest rate on loan repayments?
4. Can you explain the difference between present value and future value?
5. What factors should you consider when choosing a loan or investment?

Tip: Always check if you have the correct compounding period as it significantly affects interest calculations!