Question

You recently got promoted at your job. You have since decided to buy your dream car and expect that it will cost you $94,000 six years from today. After budgeting your expenses, you find you can start with $2000 today and decide that you can save $12,000 per year at the beginning of each year. Given a market interest rate of 6%, will you be able to purchase your car at the end of year 6? Would you be able to afford it at the end of year 7, if the overall market rate fell to 11% but your savings remained the same?

use financial calc

Answer 1

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$             2,000.00
Int Rate	11.0000%
Periods	7

Future Value = Present Value * ( 1 + r )^n
= $ 2000 ( 1 + 0.11) ^ 7
= $ 2000 ( 1.11 ^ 7)
= $ 2000 * 2.0762
= $ 4152.32

FV of Annuity Due:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the begining of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity DUe = ( 1 + r ) * FV of Annuity

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

Particulars	Amount
Cash Flow	$    12,000.00
Int Rate	11.000%
Periods	7

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.11 ) * [12000 * [ [(1+0.11)^7] - 1 ] / 0.11 ]
= ( 1.11 ) * [12000 * [ [( 1.11 ) ^ 7 ] - 1 ] / 0.11 ]
= ( 1.11 ) * [12000 * [ [ 2.0762 ] - 1 ] / 0.11 ]
= ( 1.11 ) * [ $ 117399.29 ]
= $ 130313.21

Available amount after 7 Years = Future Value + Future value of annuity due

= $ 4152.32 + $ 130313.21

= $ 134465.53

As Available amount > Cost, we can able to purchase the car.