You borrow $100,000 at a mortgage rate of 8% per year. What's the annual payment you must make to repay the loan in 25 years?
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A. B. C. D.C
If P is the annual payment, then using the annuity formula,
100,000 = P/0.08*[1 - 1/1.08^25] = 10.67P
This gives P = $9,368
To calculate the annual payment required to repay the loan in 25 years, we can use the formula for the periodic payment on an amortizing loan. This formula is commonly known as the mortgage payment formula. It takes into account the loan amount, the interest rate, and the loan term.
The mortgage payment formula is:
PMT = (P * r) / (1 - (1 + r)^(-n))
Where: PMT = Periodic payment P = Loan amount r = Interest rate per period n = Total number of periods
In this case, the loan amount (P) is $100,000, the interest rate (r) is 8% per year, and the loan term (n) is 25 years.
First, we need to convert the annual interest rate to a periodic interest rate. Since we want to calculate the annual payment, the periodic interest rate should be the same as the annual interest rate. Therefore, r = 8% per year.
Next, we need to calculate the total number of periods (n). Since the loan term is 25 years and we want the annual payment, the number of periods will be 25.
Now we can substitute the values into the formula and solve for the periodic payment (PMT):
PMT = (100,000 * 0.08) / (1 - (1 + 0.08)^(-25)) = (8,000) / (1 - (1.08)^(-25)) = 8,000 / (1 - 0.103182) = 8,000 / 0.896818 ≈ 8,920.16
Therefore, the annual payment you must make to repay the loan in 25 years is approximately $8,920.16.
None of the given answer choices matches the calculated value of $8,920.16. However, among the options provided, the closest answer is C. $9,368.