Question

You plan to buy an Audi A8 on your 26th birthday. You have priced these cars and found that they currently sell for $85,100. You believe that the price will increase by 8% per year until you are ready to buy. You can presently invest to earn 10% annually. If you have just turned 20 years old, how much must you invest per year to be able to purchase the Audi according to your plans?

Please solve with excel using present or future value calculations.

Answer 1

$ 15,911.43 needs to be invested every year starting today uptill 26th birthday to be able to purchase Audi A8 on your 26th Birthday.

USING EXCEL WE GET,

Particulars	in formulae	Values
PV OF AUDI (Price Today)	PV	85100
GROWTH RATE P.A.	RATE	8%
YEARS (20-26)	NPER	6
FV OF AUDI	$135,043.00
Formulae Used	"=-FV(C4,C5,0,C3)"
	"=FV(RATE,NPER,PMT,PV)
**Here, PMT is to be kept '0' as we are computing FV with the help of Present Value
**As no periodic cash flow is there, we can ignore "type".
NOW, TO CALCULATE PAYMENT P.A. TO ACHIEVE THE DESIRED FV
Particulars	in formulae	Values
RATE OF INTEREST	RATE	10%
FUTURE VALUE	FV (CALCULATED ABOVE)	135043
YEARS (20-26)	NPER	6
Amount to be Invested Per Year	$15,911.43
Formulae Used	"=-PMT(C14,C16,0,C15,1)"
	"=PMT(RATE,NPER,PV,FV,type)
**Here, PV is to be kept '0' as we are computing Periodic payments with the help of FV
**As periodic cash flow is there beginning today, we have taken "type"= 1, .
(in case amount needs to be invested at the end of each period, type can be taken as "0")