Question

Please solve an explain. dont copy the answer that is on chegg, it is wrong . thank you !!

please solve ASAP. comments are turned off so i cant comment on this even if it is wrong . i will dislike or like depending on if it is right. please helpYou have your eye on a nice, reliable used sedan after you are finished with school. You will probably only keep the car for about 3 years before selling it. You and the dealer determine that you can either buy the $13,000 car (with 36 monthly payments) or lease it (for 36 months). If you buy it, you must make a down payment of $3,000 at n=0, and then you must pay off the balance in monthly installments based on a 1% effective monthly interest. You would plan to sell the car for $7,000 at the end of year 3. If you choose to lease the car, you must pay $1,500 at n=0 as an origination fee, and you will make 36 end-of- month lease payments of $250 each. At the end of the lease, you will return the car to the dealership. When considering the lease, use the same effective monthly interest rate as the buy option for determining equivalence. a. What will be the monthly payment amount if you choose the buy option? b. Which option is better (e.g. which option has the lowest equivalent cost)?

Answer 1

a. Monthly payment amount if you choose the buy option can be calculated using the present value of an annuity formula. Here, we have, PV = $10,000, N = 36 months, and i = 1% per month.The formula is given by,

PV = PMT[(1 - (1+i)^-N)/i]

where PMT is the monthly payment amount. By substituting the values we get,

$10,000 = PMT[(1 - (1+0.01)^-36)/0.01]

On solving the above equation we get,

PMT = $306.87 (rounded to nearest cent)

Therefore, the monthly payment amount for the buy option will be $306.87.

b. To compare the two options, we need to find out which option has the lowest equivalent cost. The equivalent cost of the buy option is,

PV of payments + PV of residual value = $3,000 + $7,000/(1+0.01)^36 = $3,000 + $5,077.89 = $8,077.89

The equivalent cost of the lease option is,

PV of lease payments + origination fee = $250[(1 - (1+0.01)^-36)/0.01] + $1,500/(1+0.01)^36 = $7,508.51

Since the equivalent cost of the lease option is lower than the equivalent cost of the buy option, it is better to choose the lease option. Therefore, the lease option is the better option.

Step-by-step explanation:

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