Monthly payments on a house valued at $84000 with 4.9% compound interest over 30 years
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To calculate the monthly payments on a house loan, you can use the formula for a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
M = Monthly payment
P = Principal amount (loan amount)
i = Interest rate per period (monthly interest rate)
n = Total number of periods (number of months)
Let's break down the information you provided:
Principal amount (P) = $84,000
Interest rate per period (i) = 4.9% per annum, compounded monthly
Total number of periods (n) = 30 years, which is equivalent to 360 months
First, we need to convert the annual interest rate to a monthly rate:
Monthly interest rate (i) = (4.9% / 100) / 12 = 0.00408
Now, let's substitute these values into the formula:
M = $84,000 [ 0.00408(1 + 0.00408)^360 ] / [ (1 + 0.00408)^360 – 1 ]
To simplify the calculation, let's break the formula into smaller steps:
Step 1: Calculate the numerator:
Numerator = $84,000 * [0.00408 * (1 + 0.00408)^360]
Step 2: Calculate the denominator:
Denominator = (1 + 0.00408)^360 - 1
Step 3: Divide the numerator by the denominator to calculate the monthly payment:
Monthly payment (M) = Numerator / Denominator
Now, let's perform the calculations:
Step 1:
Numerator = $84,000 * [0.00408 * (1.00408)^360]
Numerator ≈ $84,000 * [0.00408 * 4.71489]
Numerator ≈ $165.02
Step 2:
Denominator = (1 + 0.00408)^360 - 1
Denominator ≈ 1.175788 - 1
Denominator ≈ 0.175788
Step 3:
Monthly payment (M) = Numerator / Denominator
M ≈ $165.02 / 0.175788
M ≈ $938.93
Therefore, the monthly payment on a house valued at $84,000 with a 4.9% compound interest over 30 years would be approximately $938.93.