Question

A property was purchased for ​$8336.00 down and payments of $1217.00 at the end of every year for 7 years. Interest is 9 % per annum compounded semi-annually.What was the purchase price of the​ property? How much is the cost of​ financing?

1)The purchase price of the property was ? $

2)The cost of financing is ? $

Answer 1

Annual interest rate = 9.00%
Semiannual interest rate = 9.00% / 2
Semiannual interest rate = 4.50%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.0450)^2 - 1
Effective annual rate = 1.092025 - 1
Effective annual rate = 0.092025 or 9.2025%

Down payment = $8,336.00
Annual payment = $1,217.00
Number of payments = 7

Purchase price of property = $8,336.00 + $1,217.00/1.092025 + $1,217.00/1.092025^2 + … + $1,217.00/1.092025^6 + $1,217.00/1.092025^7
Purchase price of property = $8,336.00 + $1,217.00 * (1 - (1/1.092025)^7) / 0.092025
Purchase price of property = $8,336.00 + $1,217.00 * 4.998937
Purchase price of property = $14,419.71

Total amount paid = $8,336.00 + $1,217.00 * 7
Total amount paid = $16,855.00

Cost of financing = Total amount paid - Purchase price of property
Cost of financing = $16,855.00 - $14,419.71
Cost of financing = $2,435.29