Sara wants new furniture for her apartment. She picked out furniture that costs $3,500. She has $500 to put down on the furniture, and she can obtain a loan at 8% for 3 years for the remainder. Approximately what will her monthly payment be?
What will be the total cost of the item?
To calculate the total cost of the item, we need to consider the down payment and the loan amount.
The price of the furniture is $3,500, and Sara has $500 for the down payment. Thus, the loan amount will be $3,500 - $500 = $3,000.
Now, let's calculate the total cost of the loan. We know that the loan term is 3 years and the interest rate is 8%.
The formula to calculate the monthly payment on a loan is:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
To calculate the monthly interest rate, we need to divide the annual interest rate by 12:
Monthly Interest Rate = Annual Interest Rate / 12
Substituting the given values into the formula:
Monthly Interest Rate = 8% / 12 = 0.08 / 12 = 0.0067
Number of Months = 3 years * 12 months/year = 36
Now, let's plug in all the values into the formula:
Monthly Payment = (3,000 * 0.0067) / (1 - (1 + 0.0067)^(-36))
After calculating, the approximate monthly payment for Sara will be $90.88.
To calculate the total cost of the furniture, we need to consider the down payment and the loan amount.
The furniture costs $3,500, and Sara is putting down $500 as a down payment. So, the loan amount will be the difference between the furniture cost and the down payment: $3,500 - $500 = $3,000.
Now, we'll calculate the total cost of the loan over 3 years with an interest rate of 8%. To do this, we can use a loan payment calculator or the formula for calculating loan payments.
Using the formula, the monthly payment (P) can be calculated using the following formula:
P = (A * r) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
A = Loan amount
r = Monthly interest rate (8% divided by 12 to get the monthly rate)
n = Total number of payments (3 years, so 3 * 12 = 36 monthly payments)
Let's calculate it step by step.
First, let's calculate the monthly interest rate:
Monthly interest rate = 8% / 12 = 0.08 / 12 = 0.0067
Next, let's calculate the total cost of the loan:
P = (3000 * 0.0067) / (1 - (1 + 0.0067)^(-36))
P ≈ $
Based on these calculations, Sara's monthly payment will be approximately $92.96.