Question

You are buying a house that cost 650,000 and you put down a down payment. you take out a loan for the remainder of the amount, on a 15-year loan, at 5.25%. find the monthly payment, total payments, and interest over the life of the loan.

Answer 1

Answers:

Monthly Payment = $4,702.68

Total Payments = $846,482.40

Interest = $261,482.40

Delete the dollar signs and/or commas if needed.

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Explanation:

The down payment is 10% of the home's value

This means that the buyer pays $65,000 up front (since 0.10*650,000 = 65,000).

The remaining 650,000 - 65,000 = 585,000 dollars is loaned in the mortgage.

Or you could write it like this 95% of 650,000 = 0.95*650,000 = 585,000

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The monthly payment formula is

P = (L*i)/( 1-(1+i)^(-n) )

where,

• P = monthly payment
• L = amount loaned
• i = interest rate per month in decimal form
• n = number of months

In this case,

• L = 585,000 dollars
• i = 0.0525/12 = 0.004375 exactly
• n = 15*12 = 180 months (equivalent to 15 years)

So,

P = (L*i)/( 1-(1+i)^(-n) )

P = (585000*0.004375)/( 1-(1+0.004375)^(-180) )

P = 4702.6846353538

P = 4702.68

The monthly payment is $4,702.68

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Let's now compute the total amount paid back (principal + interest)

If you pay 4,702.68 dollars per month over the course of 180 months, then you pay back a total of 4702.68*180 = 846,482.40

The total payments add up to 846,482.40 dollars.

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To compute the interest only, subtract the total payments from the amount loaned.

846,482.40 - 585,000 = 261,482.40 is the amount of interest only.