$PMT = $81,000 \times \frac{(0.0050000)}{\left[(1.0050000)^{(204)}-1\right]}$
Answer (2)
Calculate 1.00 5 204 ≈ 2.76615555 .
Subtract 1: 2.76615555 − 1 = 1.76615555 .
Divide 0.005 by the result: 1.76615555 0.005 ≈ 0.002831 .
Multiply by 81,000: PMT = 81 , 000 × 0.002831 ≈ 229.31 . The final answer is 229.31 .
Explanation
Understanding the Formula We are given the formula for calculating the payment (PMT): PMT = 81 , 000 × ( 1.00 5 204 − 1 ) 0.005 Our goal is to calculate the value of PMT.
Calculating the Exponent First, we need to calculate 1.00 5 204 .
1.00 5 204 ≈ 2.76615555
Subtracting 1 Next, we subtract 1 from the result: 2.76615555 − 1 = 1.76615555
Dividing Now, we divide 0.005 by the result from the previous step: 1.76615555 0.005 ≈ 0.002831
Calculating PMT Finally, we multiply 81,000 by the result from the previous step to find the value of PMT: PMT = 81 , 000 × 0.002831 ≈ 229.31 Therefore, the value of PMT is approximately $229.31.
Final Answer The payment (PMT) is approximately $229.31.
Examples
This formula is used to calculate loan payments. For example, if you borrow $81,000 at an interest rate of 0.5% per month for 204 months, the monthly payment would be approximately $229.31. Understanding loan payment calculations is essential for managing personal finances, making informed decisions about borrowing, and planning for long-term investments.
To calculate PMT using the formula provided, we first find ( 1.005 ) 204 which is approximately 2.766. Subtracting 1 and dividing 0.005 by this result gives approximately 0.002831, which is then multiplied by 81,000, resulting in a monthly payment of approximately $229.31.
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