You are interested in leasing a car, and have been offered a 36-month lease with an...

You are interested in leasing a car, and have been offered a 36-month lease with an annual interest rate of 3%, monthly payments of $400, and an optional lease buyout of $10,000.

a) What is the present value of the lease?
b) What is the future value of the lease?

Solutions

Expert Solution

Part A:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$ 400.00
Int Rate	0.2500%
Periods	36

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 400 * [ 1 - [(1+0.0025)^-36]] /0.0025
= $ 400 * [ 1 - [(1.0025)^-36]] /0.0025
= $ 400 * [ 1 - [0.914]] /0.0025
= $ 400 * [0.086]] /0.0025
$13,754.59

PV of Lease rentals is $ 13754.59

Part B:

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$ 400.00
Int Rate	0.250%
Periods	36

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 400 * [ [ ( 1 + 0.0025 ) ^ 36 ] - 1 ] / 0.0025
= $ 400 * [ [ ( 1.0025 ) ^ 36 ] - 1 ] / 0.0025
= $ 400 * [ [1.0941] - 1 ] / 0.0025
= $ 400 * [0.0941] /0.0025
= $ 15048.22
FV of Lease rentals is $ 15048.22

jeff jeffy answered 1 year ago

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