Question

In: Finance

you are thinking about leasing a car the purchase price of the car is 26000. the...

you are thinking about leasing a car the purchase price of the car is 26000. the residual value. the residual value ( the amount you could pay to keep the car at the end of the lease) os 13,000 at the end of 36 months. assume the first lease payment is due one month aftrr you get the car . the interest rate implicit in the lease 6% apr compounded monthly . what will be your lease payments for a 36 month lease

Solutions

Expert Solution

Given

Purchase Price of a Car = $ 26000

Residual Value of Car at the end of 36 Months = 13000

Interest rate = 6% Compounded monthly

Interest rate per month = 6% /12 = 0.5% per Month

Computation of Present Value of Residual Value

We know that Present Value = Future Value / ( 1+i/12)^12n When interest is compounded monthly

Here I = Interest rate

n =No.of Years

Time period = 36 Months or 36/12 =3 Years

Present Value of Residual Value = 13000/ ( 1+0.06/12)^12*3

= 13000/ ( 1.005)^36

= 13000/1.196681

= 10863.38

Hence the Present Value of residual Value is 10863.38

Computation of Present value of lease payments

Purchase Price - Present Value of Residual Value = PV of Lease payments

26000-10863.38 = PV of Lease payments

15136.62 = PV of Lease payments

Computation of Lease payment amount

We know that Present Value of Ordinary Annuity = C [ {1- ( 1+i)^n }/i]

Here C = Cash Flow per period

I = Interest rate per period

n = No.of Payments

PV of Lease payments = C [ { 1-(1+0.005)^-36 }/0.005]

15136.62 = C [ { 1-(1.005)^-36 } /0.005]

15136.62= C [ { 1-0.835645}/0.005]

15136.62 = C [ 0.164355/0.005]

15136.62= C [ 32.87102]

15136.62/32.87102= C

C = 460.4853

Hence Lease payment amount should be 460.4853 per month

Lease payments during 36 months = 460.4853*36=16577.47

If you are having any doubts,please post a comment.

Thank you.please rate it.


Related Solutions

You are thinking about leasing a car. The purchase price of the car is $35,000.
You are thinking about leasing a car. The purchase price of the car is $35,000.The residual value (the amount you could pay to keep the car at the end of the lease) is $15,000 at the end of 36 months. Assume the first lease payment is due one month after you get the car. The interest rate implicit in the lease is 7% APR, compounded monthly. What will be your lease payments for a 36-month lease? (Note: Be careful not...
You are about to buy a home; the purchase price of the car is $200,000 and...
You are about to buy a home; the purchase price of the car is $200,000 and you are paying 10% of that amount as a down payment and financing the remainder. Your mortgage loan terms are 30 years of monthly payments at an annual rate of 3.25%. How much are your monthly mortgage payments? Over the life of the loan, how much did you pay in interest a) Suppose on January 1 you deposit $2,750 in an account that pays...
Juan is leasing a new car. The price of the car is 35,000. The terms of...
Juan is leasing a new car. The price of the car is 35,000. The terms of the lease go as follows. There are 120 monthly payments with the first payment being one month from now. The nominal rate of interest is 8.4% convertible monthly. The payments in the first year are X. In the second year, the payments are 1.01X, in the third 1.01 X^2 and so on. Just after his 60th payment, Juan sells his car for Y dollars....
You purchase an antique car today for $41,774 You expect the price of the car to...
You purchase an antique car today for $41,774 You expect the price of the car to rise by 4% per year for the next 7 years. What do you expect the price of the car to be in year 7?
You purchase an antique car today for $46,260 You expect the price of the car to...
You purchase an antique car today for $46,260 You expect the price of the car to rise by 6% per year for the next 9 years. What do you expect the price of the car to be in year 9?
Option 2: Evaluate buying a car vs leasing Purchase a car for $28,988 with a 60...
Option 2: Evaluate buying a car vs leasing Purchase a car for $28,988 with a 60 month loan at 3.9% interest rate or lease a car for $259 a month for 39 months. Determine cash flows (include all relevant expenses/costs) List and explain assumptions Compute IRR, NPV, Payback, Discounted Payback to make decision
You are about to buy a home; the purchase price of the car is $200,000 and you are paying 10% of that amount as a down payment and financing the remainder.
You are about to buy a home; the purchase price of the car is $200,000 and you are paying 10% of that amount as a down payment and financing the remainder. Your mortgage loan terms are 30 years of monthly payments at an annual rate of 3.25%.How much are your monthly mortgage payments?Over the life of the loan, how much did you pay in interest?
Suppose that you are thinking about buying a car and have narrowed down your choices to...
Suppose that you are thinking about buying a car and have narrowed down your choices to two options. The new car option: the new car costs $26,000 and can be financed with a four-year loan at 7.54%. The used car option: a three-year old model of the same car costs $14,000 and can be financed with a three-year loan at 7.07%. What is the difference in monthly payments between financing the new car and financing the used car? Use PMT...
You are thinking about opening a car dealership. You bought some real estate last year for...
You are thinking about opening a car dealership. You bought some real estate last year for $700,000 which you will use for the dealership. The market value of this real estate today is $1,200,000. To build the necessary showroom and shop it will cost you $600,000, a cost which you will depreciate over 3 years. You estimate an increased need for net working capital in year zero in the amount of $40,000 which will be recovered at the end of...
You are about to purchase a brand new car for $23.400. You have $14.400 to put...
You are about to purchase a brand new car for $23.400. You have $14.400 to put down and will need to finance the rest. The dealership has two options. 1) Full price of the car and a loan of 0% interest for 3 years. 2) $1000 off the price of the car (known as cash back) and a loan for the rest with an interest rate of 5.9% for 3 years Which is the better option? (you must show work...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT