Question

Marta Alicia will buy new industrial equipment for her business. The value of It is Q 250,000 of which you will pay 20% in cash and the rest will be financed for 5 years through monthly payments at a rate of 12% annually compounded monthly. What is the value of the monthly payments?

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Answer to a math question Marta Alicia will buy new industrial equipment for her business. The value of It is Q 250,000 of which you will pay 20% in cash and the rest will be financed for 5 years through monthly payments at a rate of 12% annually compounded monthly. What is the value of the monthly payments?

Expert avatar
Jon
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110 Answers
To calculate the value of the monthly payments, we first find the monthly interest rate, the present value of the loan, and the total number of payments:

Given:
- Total value of the equipment, Q = \$250,000
- Down payment = 20\% of Q
- Annual interest rate = 12\% or 0.12 as a decimal
- Loan term = 5 years or 60 months

1. Monthly interest rate, r = \frac{0.12}{12} = 0.01
2. Amount financed, PV = Q - \text{Down payment}
= 250,000 - (0.20 \times 250,000) = 250,000 - 50,000 = \$200,000
3. Total number of payments, n = 5 \times 12 = 60

Now, we can use the formula for an amortizing loan:

P = \frac{rPV}{1 - (1 + r)^{-n}}
P = \frac{0.01 \times 200,000}{1 - (1 + 0.01)^{-60}}
P = \frac{2,000}{1 - 1.01^{-60}}
P = \frac{2,000}{1 - 0.54703}
P = \frac{2,000}{0.45297}
P \approx \$4,448.89

Therefore, the value of the monthly payments Marta Alicia would have to make for the industrial equipment is approximately \$4,448.89.

\boxed{\text{Answer: \$4,448.89}}

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