A house and lot can be acquired by a downpayment of P500,000 and a yearly payment of P100,000 at the end of each year for a period of 10 years, starting at the end of 5 years from the date of purchase. If money is worth 14% compounded annually, what is the cash price of the property?

Answer: Value of annuity of P100,000 at the end of 5 years = Annuity * [(1 + Interest rate) ^number of periods -1] / (1 + Interest rate) ^number of periods * interest rate

= P100,000 * [(1 + 0.14)^10 -1 / (1 + 0.14)^10 * 0.14

= P521,611.56

Present value of yearly payments = Value of annuity of P100,000 at the end of 5 years / (1 + Interest rate) ^number of periods

= P521,611.56 / (1 + 0.14) ^4

= P308,835.92

Cash price of property = Downpayment + Present value of yearly payments

= P808,835.92.

My question is why the period became 4 years instead of 5 years?