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MM150 Survey of Mathematics
三 Homework: Unit 6 Lab
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Brylon Beckworth $\quad 07 / 16 / 23$ 3:24 PM
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Question $14,8.7 .3$, Part 1 of 3
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Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ 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.
$\$ \square$ (Round to the nearest dollar as needed.)
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Final Answer: The monthly payment for the 20-year option is \(\boxed{385}\).
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 ：\(PMT = 385\)
Step 10 ：Final Answer: The monthly payment for the 20-year option is \(\boxed{385}\).
