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MM150 Survey of Mathematics
三 Homework: Unit 6 Lab
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Brylon Beckworth $07 / 16 / 23$ 3:24 PM
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Question $14, 8.7 .3$ , Part 1 of 3
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Use PMT $= \frac{P (\frac{r}{n})}{[1 - {(1 + \frac{r}{n})}^{- n t}]}$ to determine the regular payment amount, rounded to the nearest dollar. The price of a small cabin is $$ 45, 000$ . The bank requires a $5 %$ down payment. The buyer is offered two mortgage options: 20 -year fixed at $9 %$ or 30 -year fixed at $9 %$ . Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20 -year option?
Find the monthly payment for the 20 -year option.
$$ ◻$ (Round to the nearest dollar as needed.)
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Final Answer: The monthly payment for the 20-year option is $385$ .

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Step 1 ：The question is asking for the monthly payment for a 20-year mortgage option on a small cabin priced at $45,000 with a 5% down payment and a fixed interest rate of 9%.

Step 2 ：To solve this, we can use the PMT formula given in the question. The PMT formula is used to calculate the monthly payment for a loan with a certain interest rate and a certain number of payments.

Step 3 ：In this case, the principal P is the price of the cabin minus the down payment, the rate r is the annual interest rate divided by 100 to convert it to a decimal, n is the number of payments per year (which is 12 for monthly payments), and t is the number of years for the mortgage.

Step 4 ：We can plug these values into the PMT formula and calculate the monthly payment.

Step 5 ： $P = 42750.0$

Step 6 ： $r = 0.09$

Step 7 ： $n = 12$

Step 8 ： $t = 20$

Step 9 ： $P M T = 385$

Step 10 ：Final Answer: The monthly payment for the 20-year option is $385$ .

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