Question

a. You've just been hired at a new job. You expect to work there for 4 years. Your boss offers you a hiring bonus of either $2,739 today, or an additional $22 per month, starting next month, on your salary.

If your investments earn 2.75% APR (compounded monthly), how much would you gain or lose by taking the cash-bonus today?

b.

You purchase an antique car today for $52,394

You expect the price of the car to rise by 4% per year for the next 6 years.

What do you expect the price of the car to be in year 6?

If you would lose money, indicate your answer with a negative number.

Answer 1

Part A:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

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

Particulars	Amount
Cash Flow	$                 22.00
Int Rate	0.2292%
Periods	48

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 22 * [ 1 - [(1+0.0023)^-48]] /0.0023
= $ 22 * [ 1 - [(1.0023)^-48]] /0.0023
= $ 22 * [ 1 - [0.8959]] /0.0023
= $ 22 * [0.1041]] /0.0023
= $ 998.91
Gain by taking Bonus Today = Bonus Today - PV of additional salary

= $ 2739 - $ 998.91

= $ 1740.09

Part B:

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	$          52,394.00
Int Rate	4.0000%
Periods	6

Future Value = Present Value * ( 1 + r )^n
= $ 52394 ( 1 + 0.04) ^ 6
= $ 52394 ( 1.04 ^ 6)
= $ 52394 * 1.2653
= $ 66295.12