I keep getting the wrong answer on this. My answers have been $243.18 and another was $247.23. ugh.. neither is right, so help plz.
A homeowner planning a kitchen remodeling can afford a $200 monthly payment. How much can the homeowner borrow for 3 years at 5%, compounded monthly, and still stay within the budget? (Round your answer to the nearest cent.)
so you are looking for the Present Value of 36 payments of $200 at a monthly rate of .00416666
PV = 200 (1 - 1.00416666^-36)/.00416666
= 6673.14
thank you so much. I am not sure where my figures were coming from at all. Thanks again!
To calculate the amount that the homeowner can borrow, we will use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value,
P is the monthly payment,
r is the monthly interest rate, and
n is the number of periods.
In this case, the monthly payment is $200, the interest rate is 5% (or 0.05), and the number of periods is 3 years, which is 36 months.
First, let's convert the annual interest rate to a monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / 12 = 0.05 / 12 ≈ 0.004167
Now, let's plug the values into the formula:
FV = 200 * ((1 + 0.004167)^36 - 1) / 0.004167
Using a calculator, we find:
FV ≈ 7273.09
So, the homeowner can borrow up to approximately $7273.09 and still stay within the $200 monthly payment budget.
Therefore, the correct answer, rounded to the nearest cent, is $7273.09.