giselle wants to buy a condo that has a purchase price of $163,000. giselle earns $2,986 a month and wants…

Explanation:

Step1: Calculate Giselle's maximum mortgage payment

Her monthly income is $$2,986$, and she wants to spend no more than 25% on mortgage. So the maximum payment is $2986\times0.25=$746.5$.

Step2: Calculate the loan - amount for 20% down

The purchase price is $$163,000$. With 20% down, the down - payment is $0.2\times163000 = $32,600$, and the loan amount $L=163000 - 32600=$130,400$.

Step3: Use the mortgage - payment formula $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$

For a 30 - year loan ($n = 30\times12=360$ months) and an annual interest rate of 6.25% ($r=\frac{0.0625}{12}$), $M = 130400\times\frac{\frac{0.0625}{12}(1+\frac{0.0625}{12})^{360}}{(1+\frac{0.0625}{12})^{360}-1}\approx$804.77>$746.5$.

Step4: Analyze each option

• Option a: A 15 - year loan ($n = 15\times12 = 180$ months) with the same loan amount and interest rate will have a higher monthly payment because the loan is paid off in a shorter time.
• Option b: Lowering the interest rate to 5.5% ($r=\frac{0.055}{12}$), using the mortgage - payment formula with $L = 130400$ and $n = 360$, $M=130400\times\frac{\frac{0.055}{12}(1 + \frac{0.055}{12})^{360}}{(1+\frac{0.055}{12})^{360}-1}\approx$752.79>$746.5$.
• Option c: If the down - payment is 18% instead of 20%, the down - payment is $0.18\times163000=$29,340$, and the loan amount is $163000 - 29340=$133,660$. Using the mortgage - payment formula with $n = 360$ and $r=\frac{0.0625}{12}$, the monthly payment will be even higher than with a 20% down - payment.

Answer:

None of the options will make the loan a viable option as they all result in a monthly payment higher than her budget. So the answer is D. None. This is a viable option for Giselle.