Answer:
Option D) $1,585.35
Step-by-step explanation:
This given problem involves annuities, which are sequence of equal periodic payments. Use the following amortization formula:
[tex]PMT = PV[\frac{i}{1- (1 + i)^{-n} }][/tex]
where:
PMT = value of the monthly payments
PV = Present value of the mortgage (less 10% down of $28,000) = $252,000
i = interest rate = 5.75% ÷ 12 months = 0.004791667
n = number of compounding periods = 12 months × 25 years = 300
Substitute these values into the given formula:
[tex]PMT = PV[\frac{i}{1- (1 + i)^{-n} }][/tex]
[tex]PMT = 252,000[\frac{0.004791667}{1 - (1 + 0.004791667)^{-300} }][/tex]
PMT = $252,000(0.00629106)
PMT = $1,585.35
Therefore, the monthly payment is $1,585.35.
**Quick note: for these types of problems, make sure you don't round up your decimal places until the very last step of your solution, because if you prematurely round-up your decimal values for i, you'll end up with a much different solution. Imagine that in this given problem, your solving for 25 years' worth of payments, so those differences add up.
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