Pierce Publishing sells encyclopedias under two payment plans: cash or installment. Under the installment plan, the customer pays $23/month over 2 yr with interest charged on the balance at a rate of 15%/year compounded monthly. Find the cash price for a set of encyclopedias if it is equivalent to the price paid by a customer using the installment plan. Please round the answer to the nearest cent.



a. $332.81
b. $420.19
c. $564.26
d. $474.36
e. $406.93

Please explain. Thank you

i = .15/12 = .0125

n = 24
payment = 23

PV = 23( 1 - 1.0125^-24)/.0125
= 474.36

To find the cash price for a set of encyclopedias that is equivalent to the price paid by a customer using the installment plan, we need to calculate the total amount paid by the customer using the installment plan and then determine the equivalent cash price.

In this case, the installment plan spans two years, with monthly payments of $23. To calculate the total amount paid by the customer, we first need to find the total number of months in two years, which is 2 years x 12 months/ year = 24 months.

Using the formula for the future value of an annuity, we can calculate the total amount paid by the customer using the installment plan:

Future Value = Payment × ((1 + interest rate)^number of periods - 1) / interest rate

In this case, the payment per period is $23, the interest rate is 15% per year, compounded monthly, and the number of periods is 24.

Future Value = $23 × ((1 + 0.15/12)^(24) - 1) / (0.15/12)

Now we can calculate the Future Value:

Future Value = $23 × (1.0125^(24) - 1) / 0.0125

Using a calculator, the Future Value is approximately $564.27.

Therefore, the cash price for a set of encyclopedias that is equivalent to the installment plan payment is approximately $564.27.

Now, we compare the options given and round to the nearest cent:

a. $332.81 (Not equivalent)
b. $420.19 (Not equivalent)
c. $564.26 (Not equivalent)
d. $474.36 (Not equivalent)
e. $406.93 (Not equivalent)

None of the options given match the calculated cash price of $564.27.