Questions: Use PMT = (P(r/n))/(1-(1+(r/n))^(-nt)) to determine the regular payment amount, rounded. The price of a small cabin is 65,000. The bank requires a 5% down payment. The buyer is offered a choice between a 20-year fixed at 8.5% or a 30-year fixed at 8.5%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20-year option? Find the monthly payment for the 20-year option. (Round to the nearest dollar as needed.)

Use PMT = (P(r/n))/(1-(1+(r/n))^(-nt)) to determine the regular payment amount, rounded. The price of a small cabin is 65,000. The bank requires a 5% down payment. The buyer is offered a choice between a 20-year fixed at 8.5% or a 30-year fixed at 8.5%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20-year option? Find the monthly payment for the 20-year option. (Round to the nearest dollar as needed.)
Transcript text: Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to determine the regular payment amount, rounded. The price of a small cabin is $\$ 65,000$. The bank requires a $5 \%$ down payment. The buyer is offered a choice between a 20-year fixed at $8.5 \%$ or a 30-year fixed at $8.5 \%$. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20-year option? Find the monthly payment for the 20-year option. $\$ \square$ (Round to the nearest dollar as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Principal (P)

Principal (P) = Home Price - (Down Payment Percentage * Home Price) = 61750

Step 2: Convert Annual Interest Rate to Decimal and Monthly Rate (r/n)

Monthly Interest Rate = Annual Interest Rate / 12 = 0.00708

Step 3: Calculate Monthly Payment (PMT) for Both Options

Option 1: PMT = 536, Option 2: PMT = 475

Step 4: Calculate Total Payment Over the Loan Term for Both Options

Option 1: Total Payment = PMT * 12 * Term Years = 128640 Option 2: Total Payment = PMT * 12 * Term Years = 171000

Step 5: Calculate Total Interest Paid for Both Options

Option 1: Total Interest = Total Payment - P = 66861 Option 2: Total Interest = Total Payment - P = 109179

Step 6: Compare Interest Paid Between Options

Interest Savings with Shorter-Term Option = 42318

Final Answer:

The savings in interest with the shorter-term option (Option 1) compared to the longer-term option (Option 2) is $42318.

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