Question

A property was purchased for $7261.00 down and payments of $876.00 at the end of every month for 5 years. Interest is 3% per annum compounded quarterly. What was the purchase price of the property? How much is the cost of financing? The purchase price of the property was $ . (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) The cost of financing is $ 1. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.).

Answer 1

Down Payment = $7,261.00
Monthly Payment = $876.00
Period = 5 years or 60 months

Annual Interest Rate = 3.00%
Quarterly Interest Rate = 3.00% / 4
Quarterly Interest Rate = 0.75%

Effective Annual Rate = (1 + Quarterly Interest Rate)^4 - 1
Effective Annual Rate = (1 + 0.0075)^4 - 1
Effective Annual Rate = 1.03034 - 1
Effective Annual Rate = 0.03034 or 3.034%

Monthly Interest Rate = (1 + Effective Annual Rate)^(1/12) - 1
Monthly Interest Rate = (1 + 0.03034)^(1/12) - 1
Monthly Interest Rate = 1.002494 - 1
Monthly Interest Rate = 0.002494 or 0.2494%

Present Value of Monthly Payments = $876.00/1.002494 + $876.00/1.002494^2 + … + $876.00/1.002494^59 + $876.00/1.002494^60
Present Value of Monthly Payments = $876.00 * (1 - (1/1.002494)^60) / 0.002494
Present Value of Monthly Payments = $876.00 * 55.662269
Present Value of Monthly Payments = $48,760.15

Purchase Price of Property = Down Payment + Present Value of Monthly Payments
Purchase Price of Property = $7,261.00 + $48,760.15
Purchase Price of Property = $56,021.15

Total Amount Paid = Down Payment + Total Monthly Payments
Total Amount Paid = $7,261.00 + 60 * $876.00
Total Amount Paid = $59,821.00

Cost of Financing = Total Amount Paid - Purchase Price of Property
Cost of Financing = $59,821.00 - $56,021.15
Cost of Financing = $3,799.85