I am trying to work through this problem and am having trouble. Can someone tell me what the "w" stands for in the equation and walk me through the steps? Below is what I have so far.
Suppose A is the amount borrowed, r is the interest rate (in decimal form), and m is the total number of monthly payments.
Let w = (r)/(12)
Then the formula to determine the monthly payment amount for a loan is given by
monthly payment = Aw/1- (1)/(1+w)^m
Suppose Alice buys a car and obtains a 5 year loan for $25,000 at an interest rate of 6%.
(a) What is the numerical value of w?
Still trying to figure out what w is. I think it is $483.32 the monthly payment??
(b) What is the monthly payment? (Show values substituted in the formula, and calculate the numerical amount.) Note: Since the loan is an amount in dollars and cents, it’s important to maintain a high degree of precision in intermediate calculations, and round to the nearest cent at the end.
Loan amount P = 25,000
Interest Rate = r = 0.005 per month 6% interest annually
Number of Payments: 60
Payment amount, A = $483.32
483.32 (60) = $28,999.20 Total paid all together ????
28,999.20 – 25,000 = $3,999.20 interest paid.
Can someone show me how to solve this using algebra? Thanks!
Your answers are correct, but you have probably mis-interpreted the expression for the monthly payment. For detailed solution and the answer to a post by yourself or your classmate at:
http://www.jiskha.com/display.cgi?id=1249017180
Sure! Let's go through the steps together.
(a) To find the numerical value of w, we need to substitute the values given into the equation w = (r)/(12).
In this case, the interest rate is given as 6%. To convert it to a decimal, we divide it by 100, so r = 0.06.
Substituting this value into the equation w = (0.06)/(12), we get w = 0.005.
So, the numerical value of w is 0.005.
(b) To find the monthly payment, we need to substitute the given values into the formula:
monthly payment = Aw/1- (1)/(1+w)^m
In this case, the loan amount is $25,000 (A), the interest rate per month is 0.005 (w), and the number of monthly payments is 60 (m).
Substituting these values into the formula, we get:
monthly payment = 25,000 * 0.005 / (1- (1+0.005)^(-60))
Now let's solve this algebraically step by step:
First, let's simplify the expression (1+0.005)^(-60) by calculating the value inside the parentheses:
(1+0.005) = 1.005
Now, let's calculate the power of -60 by taking the reciprocal:
(1.005)^(-60) = 1 / (1.005^60)
Next, let's substitute this into the formula:
monthly payment = 25,000 * 0.005 / (1- 1 / (1.005^60))
Now we can evaluate the expression (1.005^60) using a calculator:
(1.005^60) ≈ 1.3481
Substituting this value into the formula:
monthly payment = 25,000 * 0.005 / (1- 1 / 1.3481)
Now let's evaluate the expression (1- 1 / 1.3481):
(1- 1 / 1.3481) ≈ 0.2577
Finally, substitute this value back into the formula:
monthly payment ≈ 25,000 * 0.005 / 0.2577
Using a calculator to evaluate this expression:
monthly payment ≈ $486.54
So, the monthly payment for Alice's 5-year loan is approximately $486.54.
Note: The monthly payment you calculated, $483.32, is close but not exact. It's important to maintain a high degree of precision in intermediate calculations to get an accurate result at the end.