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?
See a similar example at:
http://www.jiskha.com/display.cgi?id=1304355816
To answer this question, we need to use the formula for calculating loan payments:
Loan Payment = (Loan Amount * Interest Rate) / (1 - (1 + Interest Rate)^(-Number of Payments))
In this case, the loan payment is given as $200, the interest rate is 5% or 0.05 (converted to decimal form), and the number of payments is 3 years or 36 months.
To find the maximum loan amount that the homeowner can borrow, we need to solve the equation for the loan amount. Rearranging the formula, we get:
Loan Amount = (Loan Payment * (1 - (1 + Interest Rate)^(-Number of Payments))) / Interest Rate
Now let's substitute the given values into the formula:
Loan Amount = ($200 * (1 - (1 + 0.05)^(-36))) / 0.05
Calculating this equation will give us the maximum loan amount that the homeowner can borrow while staying within the $200 monthly payment budget.