$85,000 \times \frac{\left(\frac{0.05}{12}\right)}{\left(1+\frac{0.05}{12}\right)^{(12 \cdot 14)}-1}
Answer (2)
Calculate the value of 12 0.05 , which is approximately 0.004167 .
Calculate ( 1 + 12 0.05 ) 12 ⋅ 14 , which is approximately 2.0108 .
Calculate ( 1 + 12 0.05 ) 12 ⋅ 14 − 1 12 0.05 , which is approximately 0.004122 .
Multiply the result by 85 , 000 to get the final answer: 350.37 .
Explanation
Understanding the Expression We are asked to evaluate the expression: 85 , 000 × ( 1 + 12 0.05 ) ( 12 ⋅ 14 ) − 1 ( 12 0.05 ) This expression is used in finance to calculate the monthly payment on a loan.
Calculating the Value Let's break down the calculation step by step. First, we calculate 12 0.05 :
12 0.05 = 0.004166666666666667 Next, we calculate 12 ⋅ 14 :
12 ⋅ 14 = 168 Then, we calculate ( 1 + 12 0.05 ) 168 :
( 1 + 12 0.05 ) 168 = ( 1 + 0.004166666666666667 ) 168 = 2.0108262454128116 Now, we calculate ( 1 + 12 0.05 ) 168 − 1 :
2.0108262454128116 − 1 = 1.0108262454128116 Next, we calculate ( 1 + 12 0.05 ) 168 − 1 12 0.05 :
1.0108262454128116 0.004166666666666667 = 0.004122040445205338 Finally, we multiply by 85 , 000 :
85 , 000 × 0.004122040445205338 = 350.37343784245377
Final Result Therefore, the value of the expression is approximately 350.37 .
Examples
This calculation is used to determine the monthly payment for a loan of $85,000 with an annual interest rate of 5% over a period of 14 years. Banks and financial institutions use this formula to calculate mortgage payments, car loan payments, and other types of installment loans. Understanding this formula helps borrowers estimate their monthly payments and plan their finances accordingly. It also allows them to compare different loan offers and choose the one that best fits their budget.
The calculation shows that the monthly payment based on an $85,000 loan at a 5% interest rate over 14 years is approximately $350.37. This involves calculating the monthly interest rate and the total number of payments. It is commonly used in finance for loan payment estimations.
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