The dealer Carga Pesada SA presents in its table for calculating installments, the coefficient 0.057 556 626 (called Capital Recovery Factor) for financing trucks in the plan (1+59) monthly and equal installments. Regarding sales carried out on credit by this reseller, the following statements were made: I. The monthly compound interest rate charged on credit sales is less than 5.6%.
Question
Answer:
Let's analyze the given information:
1. The dealer Carga Pesada SA has a "Capital Recovery Factor" of 0.057556626 for financing trucks in the plan (1+59) monthly and equal installments.
The Capital Recovery Factor (CRF) is used to calculate equal monthly payments required to repay a loan with a given interest rate and term. In this case, the CRF is 0.057556626.
Now, let's determine if the monthly compound interest rate charged on credit sales is less than 5.6%.
To find the monthly interest rate (i), you can use the formula for calculating monthly payments (PMT) based on the CRF:
PMT = Loan Amount Γ CRF
In this case, the CRF is 0.057556626. If we assume the loan amount is 1 (for simplicity), then:
PMT = 1 Γ 0.057556626 β 0.057556626
Now, we need to calculate the monthly interest rate (i) from the monthly payment (PMT) and the loan amount (L):
PMT = L Γ (i / (1 - (1 + i)^(-n)))
Where:
PMT = Monthly payment (0.057556626)
L = Loan amount (1)
i = Monthly interest rate (unknown)
n = Total number of payments (59)
Rearrange the formula to solve for i:
i = ((PMT / L) - 1) / (-n)
i = ((0.057556626 / 1) - 1) / (-59)
i β (0.057556626 - 1) / (-59)
i β (-0.942443374) / (-59)
i β 0.015982177
The calculated monthly interest rate is approximately 0.015982177 or approximately 1.5982%.
Now, let's compare this calculated monthly interest rate with 5.6%:
The calculated monthly interest rate (approximately 1.5982%) is indeed less than 5.6%.
So, Statement I is true: The monthly compound interest rate charged on credit sales is less than 5.6%.
solved
general
10 months ago
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