Question

You need a 25-year, fixed-rate mortgage to buy a new home for $315,000. Your mortgage bank will lend you the money at an APR of 6.1 percent for this 300-month loan. However, you can afford monthly payments of only $1,550, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,550?

Answer 1

To keep the monthly payments at $1,550, the balloon payment at the end of the loan will have to cover the remaining loan balance. The balloon payment can be calculated using the present value of an annuity formula. In this case, the balloon payment is approximately $204,762.65.

Step-by-step explanation:

To keep the monthly payments at $1,550, the balloon payment at the end of the loan will have to cover the remaining loan balance. To calculate the balloon payment, first determine the monthly interest rate by dividing the annual interest rate by 12. In this case, the monthly interest rate is 6.1% divided by 12, which is 0.00508. Next, calculate the remaining loan balance after 25 years by using the formula for the present value of an annuity:

Remaining Loan Balance = Monthly Payment * (1 - (1 + Monthly Interest Rate)-n)) / Monthly Interest Rate

Plugging in the values, we get:

Remaining Loan Balance = $1,550 * (1 - (1 + 0.00508)⁻³⁰⁰)) / 0.00508

Calculating this will give the value of the balloon payment, which in this case is approximately $204,762.65.

Answer 2

The answer is $1,441,746.04

Step-by-step explanation:

Solution

Given that:

The Annual rate = 6.1%

The monthly interests rate = 6.1%/12 =0.5083%

Monthly payment =$1,550

The time period = $1,441,746.04300 Months

The amount of payment at the end of 300 months is

=1,550 *((1.005083^300 - 1) / 0.005083

The amount of payment at the end of 300 months is = $1,090,754.66

Thus

Future value of $315,000 = $315,000*1.005083^300

= $1,441,746.04

Now

The balloon payment = $1,441,746.04 - 1,090,754.66

= $350,991.38

Therefore the largeness of this balloon payment will be $1,441,746.04