Question

What price will a finance company pay for a conditional sale contract requiring 21 monthly payments of $210.50, if the company requires a rate of return of 20% compounded semiannually? The first payment is due one month from now.

Answer 1

There are 2 semi annual periods in a year

There are 12 months in a year

(1 + APR/n)^n - 1 = (1 + APR/n)^n - 1

(1 + 0.2/2)^2 -1 = (1 + APR/12)^12 - 1

(1 + 0.1)^2 - 1 = (1 + APR/12)^12 - 1

1.21 - 1 = (1 + APR/12)^12 - 1

1.21 = (1 + APR/12)^12

1.01601 = 1 + APR/12

APR = 0.19214 or 19.214%

Monthly rate = 19.214% / 12 = 1.60117%

Present value = Monthly payments * [1 - 1 / (1 + rate)^time] / rate

Present value = 210.5 * [1 - 1 / (1 + 0.0160117)^21] / 0.0160117

Present value = 210.5 * [1 - 0.71635] / 0.0160117

Present value = 210.5 * 17.71498

Present value = $3,729.00

Price will be $3,729.00