Question

you plan to purchase the new Tesla Model 3 in 5 years. The car will cost $35,000. You will be able to afford payments of $550 per month and plan to take out a 3 year loan at 4.25% to finance the purchase. What down payment would you have to provide to have your desired monthly payments. How much would you need to save each month in an account earning 3.5% interest to afford this down payment in 5 years

Answer 1

Price of Car = $ 35000

PV of annuity ( EMIS ):

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	$               550.00
Int Rate	0.3542%
Periods	36

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 550 * [ 1 - [(1+0.0035)^-36]] /0.0035
= $ 550 * [ 1 - [(1.0035)^-36]] /0.0035
= $ 550 * [ 1 - [0.8805]] /0.0035
= $ 550 * [0.1195]] /0.0035
= $ 18558.93
Down Payment after 5 Years = Price - PV of EMIs

= $ 35000 - $ 18558.93

= $ 16441.07

AMount to be saved to reach Down Payment in 5 Years:

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
FV of Annuity	$      16,441.07
Int Rate	0.2917%
Periods	60

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$16441.07 = Cash Flow * [ [ ( 1 + 0.0029 ) ^ 60 ] - 1 ] / 0.0029
$16441.07 = Cash Flow * [ [ ( 1.0029 ) ^ 60 ] - 1 ] / 0.0029
$16441.07 = Cash Flow * [ [ ( 1.1909 ] - 1 ] / 0.0029
$16441.07 = Cash Flow * [ 0.1909 ] / 0.0029
Cash Flow = $ 16441.07 * 0.0029 / 0.1909
Cash Flow = $ 251.14

Monthly deposit for 5 years is $ 251.14