A lender requires that monthly mortgage payments be no more than 25% of gross monthly income with a maximum termof 30 years. If you can make only a 15% down payment, what is the minimum monthly income needed to purchase a $300,000 house when the interest rate is 6% compounded monthly?

$61,187.6

Explanation:

We first, must find the value of the monthly payments. Because the payments are regular in time, have the same value, and fall under the same interest rate, the payments are an annuity.

To find the value of the monthly payments, we use the present value of an annuity formula, but first, we substract the down payment from the total mortgage payment (300,000 x 15% = 45,000), so the mortgage payment that we will use in the formula is = 300,000 - 45,000 = 255,000

Because the lender requires the monthly payments to be no more than 25% of gross income, we need to find for what value $15,296.9 is the 25% of:

15,296.9 x 100 / 25 = 61,187.6

of the three mortgage options that demarco and tanya have to choose from, the balloon payment mortgage would be their best option, over adjustable payment and fixed payment plans.ultimately, the balloon payment plan would save demarco and tanya overall, in interest, would cost less monthly, and they would only have to make these payments for 8 years, opposing to 30 years for adjustable or fixed payment plans. 

overall, demarco and tanya would save $80,811 if they chose balloon payments over fixed payments, and would save $116,711 if they choose balloon payments over adjustable payments. benefits with choosing fixed payments over adjustable payments is that, in the end, the payments will still be $836.30 a month, while with adjustable payments, the initial monthly payments will be $763.38 to $1082.70 a month, ultimately leading to a more costly purchase. benefits with choosing fixed payments over balloon payments are not present. benefits in choosing adjustable payments over is that it has a lower interest rate, and starts with lower monthly payments initially. benefits in choosing adjustable payments over balloon payments include a lower interest rate, and lower initial monthly payments. benefits in choosing balloon payments over fixed payments include lower interest rates, lower overall price, lower monthly payments, takes less time to pay off, and does not require a downpayment. benefits in choosing balloon payments over adjustable payments include, lower monthly payments (when averaged), takes less time to pay off, and lower overall price.

hence, option c, balloon payments, is the best option for demarco and tanya to make this purchase, for it will save them a minimum of $80811, and a maximum of $116,711.