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
4.6
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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