Sarah can afford $255 per month for 6 years on a car payment, what is the price of a car that she can afford at this time?
Assume an annual interest rate of 8%.
I do not remember how to solve for problems like this one.
i = .08/12 = .00666... don't round off, carry answer in your calculator's memory
n = 72
amount accumulated
= 255( 1.00666...^72 - 1)/.0066....
= 23,466.46
To solve this problem, we can use the formula for calculating the present value of an annuity. The formula is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value (price of the car Sarah can afford)
PMT = Payment per period ($255 per month)
r = Interest rate per period (8% per year divided by 12 months equals approximately 0.67% per month)
n = Number of periods (6 years times 12 months equals 72 months)
Now let's substitute the values into the formula:
PV = $255 * (1 - (1 + 0.0083)^(-72)) / 0.0083
Calculating this equation will give us the price of the car that Sarah can afford.