Suppose Alice buys a car and obtains a 5 year loan for $25,000 at an interest rate of 6%.
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
(Aw)/1-(1)/ (1+w)^m
(a) What is the numerical value of w?
(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.
(c) If Alice makes all 60 payments, how much will have been paid altogether?
The amortization formula that you should be using is given here:
http://www.vertex42.com/ExcelArticles/amortization-calculation.html
The "A" term in that formula is the payment required per period. What you are using for A is the principal (P) in that formula. Your numerical value of w should be 0.005.
What should the set up of this equation look like? I tried to put it together and this is what I got. What am I doing wrong? Thanks!
w=(r)/(12)
(0.005)=(0.06)/(12)
m = (Aw)/1 - 1/(1+w)^m
(25000)(0.005)/1- (1)/(1+0.005)^60
Is any of this correct?
To find the answers to these questions, we can follow the given steps:
(a) Firstly, let's find the numerical value of w, which represents the monthly interest rate.
Given that r is the annual interest rate in decimal form, we need to convert it to a monthly rate by dividing it by 12. Thus, w = r/12.
In this case, r = 6%, which means r = 0.06. So, w = 0.06/12 = 0.005.
(b) Now, let's calculate the monthly payment using the formula:
Monthly payment = (Aw) / [1 - (1 + w)^(-m)]
In this case, A = $25,000, w = 0.005, and m = 5 years * 12 months/year = 60 months.
Substituting these values into the formula:
Monthly payment = ($25,000 * 0.005) / [1 - (1 + 0.005)^(-60)]
To calculate the numerical amount, we need to substitute the values and round the result to the nearest cent.
Monthly payment ≈ ($125) / [1 - (1.005)^(-60)]
By calculating this expression, the monthly payment amount will be obtained.
(c) If Alice makes all 60 payments, we can find the total amount she will have paid by multiplying the monthly payment by the total number of payments.
Total amount paid = Monthly payment * Number of payments
Substituting the previously calculated monthly payment of Alice into this formula:
Total amount paid = Monthly payment * 60
By calculating this expression, the total amount Alice will have paid over the 5-year period will be determined.