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In: Finance

john is considering buying a new car for $20,000 with $4,000 down payment and a 3-year...

john is considering buying a new car for $20,000 with $4,000 down payment and a 3-year car loan with APR 3.4%. The car's resale value will be $12,000 at the end of 3 years. The dealership also offers a lease option with $1000 security deposit which will be refunded at the end of 3-year lease. The lease monthly payment will be $300 per month and John could also invest his deposit at 1% in a saving account. Should John choose to buy or lease? Please show calculation.

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Expert Solution

Price of Car = $20,000

Down Payment = $4,000

Loan Value = Price of Car - Down Payment = $20,000 - $4,000 = $16,000

Loan Period = 3 years = 36 months

Annual interest rate = 3.4%

Monthly Interest rate = 3.4%/12 = 0.2833%

Monthly loan payment can be calculated using PMT function in spreadsheet

PMT(rate, number of periods, present value, future value, when-due)

Where, rate = Monthly Interest rate = 0.2833%

number of periods = Loan Period = 36 months

present value = Loan Value = $16,000

future value = 0

when-due = when is the payment made each month = end = 0

Monthly loan payment = PMT(0.2833%, 36, 16000, 0, 0) = $468.13

Security Deposit for Lease = $1,000

Monthly lease payment = $300

The car's resale value will be $12,000 after 3 years

Let us assume that the extra amount that he pays as down payment and the amount that he saves each month by opting for lease over loan will be deposited in the savings account which will give him 1% per year

Extra amount he requires for loan down payment over lease = down payment - security deposit for lease

= $4,000 - $1,000 = $3,000

Value of this amount after 3 years deposited in the savings account = 3000*(1+1%)³ = 3000*1.030301

= $3,090.90

Amount saved each month by going lease over loan = monthly loan payment - monthly lease payment

= $468.13 - $300 = $168.13

Future value of these monthly deposits can be calculated using FV function in spreadsheet

FV(rate, number of periods, payment amount, present value, when-due)

Where, rate = monthly deposit rate = 1%/12 = 0.0833%

number of periods = deposit period = 36 months

payment amount = monthly deposit = $168.13

present value = present value of deposits = 0

when-due = when is the deposit made each month = end = 0

Future value of these monthly deposits = FV(0.0833%, 36, 168.13, 0, 0) = $6,141.61

Total Future Value of deposits by opting for Lease = Future Value of Initial deposit + Future Value of monthly deposits + Security deposit refund = $3,090.90 + $6,141.61 + $1000 = $10,232.51

If John decides to buy he generates a future value of $12,000 (resale value of car) after 3 years

If John decides to lease he generates a future value of $10,232.51 after 3 years

Hence John should buy the car

jeff jeffy answered 1 year ago

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