Question

Is this reasonable? A lending agency advertises in the paper an APR of 12% on a home mortgage with a term of 30 years. The ad claims that the monthly payment on a principal of $100,000 will be $10, 290. Lea Macmillan Is this claim reasonable? © Yes, this sounds like a good deal. O No, this monthly payment amount is too large. It cannot be determined if this monthly payment amount is a good deal or not. • No, this monthly payment amount is too small. What should the ad have said the payment would be? (Enter your answer rounded to the nearest dollar.) The ad should have said the payment would be s per month. What do you think happened here? Nothing went wrong. The lending agency's calculations and final monthly payment value were correct. • The lending agency swapped the values for r and r in the Monthly Payment formula. The decimal point was entered in the wrong place. • The lending agency swapped the values for Amount Borrowed and in the Monthly Payment formula.

Answer 1

Answer:

To determine if the claim is reasonable, we can calculate the monthly payment using the formula for a fixed-rate mortgage:

$[ M = \frac{P \times r \times (1+r)^n}{(1+r)^n - 1}]$

Where:

- $(M)$ is the monthly payment

- $(P)$ is the principal amount (\$100,000)

- $(r)$ is the monthly interest rate (APR divided by 12, and expressed as a decimal)

- $(n)$ is the total number of payments (30 years multiplied by 12 months per year)

Let's calculate:

$\[ r = \frac{12\%}{12} = 0.01]$

$\[ n = 30 \times 12 = 360]$

Plugging these values into the formula:

$\[ M = \frac{100000 \times 0.01 \times (1+0.01)^{360}}{(1+0.01)^{360} - 1}]$

$\[ M ≈ \frac{100000 \times 0.01 \times (1.01)^{360}}{(1.01)^{360} - 1}]$

$\[ M ≈ \frac{100000 \times 0.01 \times 50.64167812755673}{50.64167812755673 - 1}]$

$\[ M ≈ \frac{5064.167812755673}{49.64167812755673}]$

$[M ≈ 102.0497762150958]$

Rounding to the nearest dollar, the monthly payment is approximately $102.

Therefore, the claim of $10,290 per month is not reasonable. The ad should have stated that the payment would be approximately $102 per month.

As for what might have happened, it's likely that there was a mistake in the calculation or in the information provided in the advertisement. One possibility is that the decimal point was misplaced, leading to an inflated monthly payment amount.