A security business invoices its 30,800 customers on the first day of each month, with each of two computers doing half the job.

One invoicing machine produces at the rate of 7,700 per hour, and the other at the rate of 6,800 per hour. When the first computer finishes its run, how many invoices did the second computer still need to produce?A. 1525
B. 1200
C. 1750
D. 1800
E. 1400

Business

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A store offers two payment plans. Under the installment plan, you pay 25% down and 25% of the purchase price in each of the next

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Answer:

a-1) Present value of the installment option is $93.08.

Present value for immediate bill payment is $90.

a2) Opting to pay the bill immediately is the preferable choice.

b-1) Present value of the installment option amounts to $88.65.

b-2) In this scenario, paying in installments is the better option.

Explanation:

a-1) To determine the present value of the installment plan, the payments occur as follows: $25 immediately, followed by $25 at the end of each of the next 3 years. This setup constitutes an annuity due, and the present value can be calculated as follows:

$Present value =PMT*\frac{[1-(1+i)^-^n]}{i}*(1+i)$

PMT denotes the annuity payment at the start of each period, which is $25.

i signifies the interest rate compounded per period.

=0.05

n represents the number of payment periods, which amounts to 4.

Present value = $25*\frac{[1-(1+0.05)^-^4]}{0.05}*(1+0.05)$ =$93.08

The present value of immediate bill payment equals $100, reduced by the 10% discount, calculated as $100 * 0.9 = $90.

a-2) Paying immediately is advantageous since it costs $90 compared to the $93.08 present value of installments.

b1) If the installment payments do not commence for another year, the present value of the payment series is computed as:

$Present value =PMT*\frac{[1-(1+i)^-^n]}{i}*\frac{(1+i)}{1+1}$

= $PMT*\frac{[1-(1+i)^-^n]}{i}$

= $25*\frac{[1-(1+0.05)^-^4]}{0.05}$ = 88.65

b-2) In this instance, paying via installments is better as it is less expensive at $88.65 compared to the immediate payment's present value at $90.

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