Jamie secured a 4-year car lease at 5.30% compounded annually that required her to make payments of $886.59 at the beginning of each month. Calculate the cost of the car if she made a downpayment of $3,000.
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Answer:
Step-by-step explanation:
Car Lease Cost Calculation
Christopher secured a 5-year car lease at 5.60% compounded annually that required her to make payments of $885.19 at the beginning of each month. Calculate the cost of the car if she made a downpayment of $1,250.
To calculate the cost of the car, we need to first calculate the total amount of payments made over the 5-year lease period.
Since the lease requires monthly payments, we first need to convert the interest rate to a monthly rate by dividing the annual rate by 12:
r = 5.60% / 12 = 0.00466667
Next, we need to calculate the total number of payments made over the 5-year lease period:
n = 5 years x 12 months/year = 60 months
Now we can calculate the total amount of payments made over the lease period using the formula for the present value of an annuity:
PMT = $885.19
PV = PMT x ((1 - (1 + r)^(-n)) / r) = $46,579.26
This is the total amount paid over the 5-year lease period. To calculate the cost of the car, we need to subtract the down payment:
Cost of car = PV - down payment = $46,579.26 - $1,250 = $45,329.26
Therefore, the cost of the car is $45,329.26.
Jamie secured a 4-year car lease at 5.30% compounded annually that required her to make payments of $886.59 at the beginning of each month. Calculate the cost of the car if she made a downpayment of $3,000
To calculate the cost of the car, we first need to calculate the total amount of payments made over the 4-year lease period.
Since the lease requires monthly payments, we first need to convert the interest rate to a monthly rate by dividing the annual rate by 12:
r = 5.30% / 12 = 0.00441667
Next, we need to calculate the total number of payments made over the 4-year lease period:
n = 4 years x 12 months/year = 48 months
Now we can calculate the total amount of payments made over the lease period using the formula for the present value of an annuity:
PMT = $886.59
PV = PMT x ((1 - (1 + r)^(-n)) / r) = $42,581.34
This is the total amount paid over the 4-year lease period. To calculate the cost of the car, we need to subtract the down payment:
Cost of car = PV - down payment = $42,581.34 - $3,000 = $39,581.34
Therefore, the cost of the car is $39,581.34.