You can purchase a residential building for $100,000 cash or $20,000 down and quarterly payments $3,000 for 10 years. The first payment would be due three months after the purchase date. If money can earn 10% compounded quarterly during the next 10 years, which option should you choose?
A) Both are equally as good so choose either one.
B) $100,000 cash
C) Neither option can earn 10% compounded quarterly so do nothing.
D) Not enough information to decide.
E) $20,000 down and $3,000 per quarter for 10 years.

Question

Quizplus · Accepted Answer

To determine the better option, calculate the present value (PV) of the $20,000 down and $3,000 quarterly payments for 10 years at a 10% annual interest rate compounded quarterly. The formula for the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the interest rate per period, and n is the total number of payments. The present value of the $3,000 quarterly payments is calculated using the quarterly interest rate (10%/4 = 2.5% or 0.025 per quarter) and the total number of payments (10 years * 4 quarters = 40). Adding the $20,000 down payment to this calculation gives the total cost in today's dollars for the financed option. If this total present value is less than $100,000, then option E is the better choice because it costs less in today's dollars than paying $100,000 upfront.

You Can Purchase a Residential Building for $100,000 Cash or $20,000