The Washington family can purchase a new home with an 80,000 loan at 6% interest. If the term of the loan is set up to be 20yrs (240 months), what will be there monthly payment toward this loan. Use formula n=-In(1-A(r/12)I P)
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In(1 + r/12)
To calculate the monthly payment on a loan, we can use the formula:
n = - [ln(1 - A(r/12) / P)] / ln(1 + (r/12))
Where:
n = monthly payment
A = loan amount
r = interest rate (as a decimal)
P = number of payment periods
In this case, the loan amount (A) is $80,000, the interest rate (r) is 6% (or 0.06 in decimal form), and the number of payment periods (P) is 240 months.
Now, let's substitute these values into the formula:
n = - [ln(1 - 80000(0.06/12) / 80000)] / ln(1 + (0.06/12))
Simplifying further:
n = - [ln(1 - 0.005) / ln(1.005)]
Using a calculator to find the natural logarithm (ln), we get:
n = - [-0.005 / 0.005002]
Finally, calculate the value of n:
n ≈ $506.69
Therefore, the Washington family will have a monthly payment of approximately $506.69 towards this loan.