Question

A local moving service recently purchased a van by securing a loan with semiannual payments of $3200 per semiannual period for 7 years at 13% per year compounded semiannually. What was the purchase price of this van? (Round your answer to the nearest cent.)

Answer 1

Present value=Payment*[1-(1+interest rate)^(-Time period)]/Interest rate
In the given question, interest rate=13% per year, so semiannual interest rate is 13%/2=0.065 and payment=$3200 per semiannual period.
Time period is 7 years, number of periods (semiannual) will be 7*2=14
Now, present value=$3200*[1-(1+0.065)^(-14)]/0.065
=$3200*[1-(1.065)^(-14)]/0.065
=$3200*[1-0.414100249]/0.065
=$3200*(0.585899751)/0.065
=$1874.879203/0.065
=$28844.29543 or $28844.30 (Rounded to the nearest cent)

Purchase price of the van was $28844.30