Part 1:

a. Beth Klemkosky purchased a yacht for $60,000 and made a down payment of $12,000. The amount she needs to borrow is:

$\text{Amount to borrow} = \text{Total price of yacht} - \text{Down payment}$

$\text{Amount to borrow} = 60,000 - 12,000 = 48,000$

So, the amount Beth needs to borrow is $48,000.

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Part 2:

b. To find Beth's equal annual payments, we will use the formula for loan amortization with equal payments, where the payments cover both the principal and interest. The formula for the payment is:

$P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}$

Where:

• $P$ = the annual payment
• $r$ = annual interest rate (in decimal form, so 8% becomes 0.08)
• $PV$ = present value of the loan (the amount borrowed, $48,000)
• $n$ = number of periods (in this case, 13 years)

Step-by-step calculation:

1. Interest rate: $r = 8\% = 0.08$
2. Loan amount (Present value, $PV$) = $48,000
3. Number of payments (years), $n = 13$

Substitute these values into the amortization formula:

$P = \frac{0.08 \cdot 48,000}{1 - (1 + 0.08)^{-13}}$

First, calculate the denominator:

$1 + 0.08 = 1.08$

$1.08^{-13} \approx 0.3495$

Now, subtract that value from 1:

$1 - 0.3495 = 0.6505$

Now, calculate the payment $P$:

$P = \frac{0.08 \cdot 48,000}{0.6505}$

$P = \frac{3,840}{0.6505} \approx 5,902.81$

So, the annual payment Beth needs to make is approximately $5,902.81.

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Final Answers:

a. Amount to borrow: $48,000

b. Annual payment: $5,902.81

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Would you like further details or have any other questions?

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Here are 5 related questions to expand on this:

1. How is the interest portion of each payment calculated over time in an amortization schedule?
2. What is the total interest paid over the life of the loan?
3. How much of the principal is repaid by the end of the 5th year?
4. How would the payments change if the interest rate were 6% instead of 8%?
5. How does the loan amortization process differ for monthly payments instead of annual payments?

Tip: The earlier payments in an amortized loan are more heavily weighted towards paying off interest, while later payments focus more on reducing the principal.