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: