Final answer:
The annual payment on a $300,000 house loan at an 8% annual interest rate over 30 years is approximately $26,645.28. Over the life of the loan, the total interest paid would be about $499,358.4.
Step-by-step explanation:
To calculate the annual payment for a $300,000 house loan at an 8% annual interest rate over 30 years, we can use the formula for an annuity which is derived from the present value of an annuity formula: PV = R * [(1 - (1 + i)^-n) / i], where PV is the present value (amount of the loan), R is the annual payment, i is the interest rate per period, and n is the number of periods.
To isolate R (the annual payment we want to find), we rearrange the formula to: R = PV * (i / (1 - (1 + i)^-n)).
Substituting the given values we get: R = 300,000 * (0.08 / (1 - (1 + 0.08)^-30)). Now, we perform the calculations:
- Calculate the denominator: (1 + 0.08)^-30 = approximately 0.099379
- Subtract from 1: 1 - 0.099379 = 0.900621
- Divide the interest rate by this number: 0.08 / 0.900621 = approximately 0.0888176
- Multiply by the principal amount: 300,000 * 0.0888176 = approximately $26,645.28
The annual payment R would be approximately $26,645.28.
To find out how much interest will be paid over the life of the loan, we multiply the annual payment by the number of payments and subtract the principal:
Total Interest Paid = (R * n) - PV = ($26,645.28 * 30) - $300,000 = $799,358.4 - $300,000 = $499,358.4 in interest paid over the life of the loan.