Straight-Line Depreciation
True/False: The equation for straight-line depreciation is given by the equation
y = A(1-r)^x
False, this is the equation for exponential decay.
What does the A and r stand for in the equation
y = A(1-r)^x?
A - initial amount.
r - interest (as a decimal).
What do P, r, t mean in the monthly payment formula?
P - principal amount
r - interest rate (as a decimal)
t - time in years.
True/False: The slope for the straight-line depreciation can be found by
y = (x_2 -x_1)/(y_2 - y_1
False, the numerator and denominator need to be switched.
True/False: The exponential decay equation can also be thought of as y = (initial amount)(percent retained)x
True. If r is the percent lost, then (1-r) is the percent retained for the vehicle.
False, you must multiply by the number of months you make the payment for.
The straight-line depreciation equation for a car is given by the equation
y = -2150x +32000
What is the original price of the car and how much value does it lose each year?
It loses $2150 each year and its original price is $32,000.
The 24 Toyota Tacoma loses value very slowly. It loses value at only 1.5% each year. What is the exponential decay equation if the starting value of a 24 Toyota Tacoma is $31,590?
The exponential decay equation is
y = 31590(0.985)^x
Baeza is considering getting a new truck. The trucks price is $32,000 and he was approved for a 4-year loan at 5.5%. What is the monthly payment?
The monthly payment is $744.21
Baeza's truck was $21,000 when he first purchased it. 5 years later, it has a value of $17,000. What is the slope for the straight-line depreciation equation?
Hint: This is how much value it loses each year.
The slope for the straight-line depreciation equation would be
m=-800
The exponential decay is equation for a vehicle is given by the equation
y = 21000(0.97)^x
What is the value of the vehicle after 5 years?
The value of the vehicle is $18,033.41
Mrs. Baeza is considering getting a new Jetta. The trucks price is $27,000 and she was approved for a 4-year loan at 4.5%.What is the total amount of interest she would pay for this vehicle?
Mrs. Baeza will pay a total amount of $2,553.12 in interest.
Mrs. Baeza's Jetta was worth $19,000 when it was first purchased. 8 years later, it has a value of $11,000. What is the straight-line depreciation equation for Mrs. Baeza Jetta?
The straight-line depreciation equation is
y = -1000x+19000
1. Find the exponential decay equation.
2. How much is the vehicle worth after 3 years?
The vehicle is worth $30,422.13
Jake was approved for two loans for the same vehicle starting at $32,000.
The first loan is for 6 years with an interest rate of 3.9%.
The second loan is for 4 years with an interest rate of 5.1%.
Which loan will Jake pay the most interest on?
Jake will pay $3,941.68 in interest for the first loan, but he pays $3,442.72 for the second loan.
Therefore he pays the most amount of interest for the first loan.