Your car lease requires a down payment of $1,500 and payments of $450 per month for 36 months. the apr is 6% compounded monthly and payments are made at the end of the month. at the end of the lease, you have the option to buy the vehicle for $20,000 (the residual value). how much is the car worth today? (round to whole number and answer without $ sign)

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Mathematics

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29 October, 23:57

Your car lease requires a down payment of $1,500 and payments of $450 per month for 36 months. the apr is 6% compounded monthly and payments are made at the end of the month. at the end of the lease, you have the option to buy the vehicle for $20,000 (the residual value). how much is the car worth today? (round to whole number and answer without $ sign)

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Lincoln Cochran · Answer 1

Monthly interest, i = APR/12 = 0.06/12 = 0.005

Monthly payment, A = $450

Period, n = 36 (months)

Future value of payment

= A ((1+i) ^n-1) / i

= 450 ((1.005^36-1) / 0.005

= 17701.2472341

Future value of car

F = future value of payment + residual value

= 17701.2472341 + 20000

= 37701.2472341

Present value of car

= downpayment + present value of future payments

= 1500 + F / (1+i) ^36

= 1500 + 37701.2472341 / (1.005^36)

= 1500 + 31504.86

= 33004.86