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A law firm buys a computerized word-processing system costing $10,000. If the firm pays 20% down and amortizes the rest with equal monthly payments over 5 years at 9% compounded monthly, what will be the monthly payment?

A. $207.58
B. $166.07
C. $2,045.22
D. $1,636.18

User Zavior
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1 Answer

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Final answer:

To find the monthly payment for the law firm's computerized word-processing system, firstly calculate the down payment and subtract it from the total cost. Then, use the formula for the payment on an amortizing loan with the appropriate monthly interest rate and number of payments to arrive at the monthly payment of approximately $166.07, which is option B.

Step-by-step explanation:

The question pertains to calculating the monthly payment on a financed purchase after a down payment has been made and the remainder is amortized with compound interest. To solve this, we can use the formula for the payment on an amortizing loan, which is:

P = (Pv x r) / (1 - (1 + r)^-n)

where:

  • P is the monthly payment
  • Pv is the present value of the loan after down payment
  • r is the monthly interest rate
  • n is the total number of payments

Firstly, calculate the down payment:

20% of $10,000 is $2,000.

Subtract the down payment from the total cost to find the amount to be financed:

$10,000 - $2,000 = $8,000

The annual interest rate is 9%, so the monthly interest rate is 9% divided by 12, which is 0.75% or 0.0075 in decimal form.

The total number of monthly payments over 5 years is 5 years x 12 months/year = 60 payments.

Inserting these values into the formula gives us:

P = ($8,000 x 0.0075) / (1 - (1 + 0.0075)^-60)

Using a calculator, we find that the monthly payment P is approximately $166.07.

The answer is option B. $166.07.

User Soob
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