Answer:
- monthly payment: $726.43
- interest paid: $162,513.69
Explanation:
You want to know the monthly payment on a 30-year loan of $99,000 at 8%, and the total interest paid.
Payment
The monthly payment is given by the amortization formula ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where P is the loan amount, r is the annual interest rate, and t is the loan period in years
A = $99000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 726.42692814058
The monthly payment is $726.43.
Interest paid
The total of monthly payments is about 360 times the "exact" value of the monthly payment. There is always a slight adjustment made in the last payment to account for the fact that the payment value is always rounded. We can approximate that adjustment by using the "exact" monthly payment amount: $726.42693
The interest paid is the difference between the total of payments and the original loan amount:
I = 360×$726.42693 -99000 ≈ $162,513.69
The total interest paid is about $162,513.69.
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Additional comment
If you use 360 times the monthly payment of $726.43, you will compute the interest paid as $162,514.80.
If you compute the future value of the loan after 360 payments of $726.43, you will find it is $4.58. This means the last payment will be $726.43 -4.58 = $721.85, and the total of payments will be $261,510.22, which includes $162,510.22 in interest.
If you make an amortization schedule, where interest is rounded every month (as in "real life"), the result will be different from any of these values. It is $162,510.63. (The last payment is $722.26.)
The upshot is that the amount you determine for total interest paid will depend on the method you use to determine it.