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Some friends tell you that they paid $25000 down on a new house and

are to pay $525 per month for 30 years. If interest is 7.8% compounded
monthly, what was the selling price of the house? How much interest
will they pay in 30 years

1 Answer

4 votes

Answer: To find the selling price of the house, we can use the formula for the present value of an annuity:

PV = A * ((1 - (1 + r)^-n) / r)

Where:

PV = Present Value

A = Annuity payment per period

r = Interest rate per period

n = Total number of periods

In this case, the annuity payment is $525 per month, the interest rate is 7.8% per year compounded monthly (which is equivalent to a monthly interest rate of 7.8% / 12 = 0.65%), and the total number of periods is 30 years * 12 months/year = 360 months.

Using these values, we can calculate the present value of the annuity:

PV = 525 * ((1 - (1 + 0.0065)^-360) / 0.0065)

PV = 525 * 162.577

PV = $85,192.25

So the selling price of the house was $85,192.25 + $25,000 down payment = $110,192.25.

To calculate the total interest paid over 30 years, we can subtract the total payments from the selling price:

Total payments = $525/month * 360 months = $189,000

Total interest paid = $189,000 - $110,192.25 = $78,807.75

Therefore, the friends will pay $78,807.75 in interest over 30 years.

Explanation:

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User Krishna Satya
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