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Question 65735: Future Value the concept called Present value You want to buy a new car in 5 years and estimate you need $20,000.00.If the bank pays you 6% interest rate how much do you need to put in the bank today? I need step by step instructions of how to get the answer. The book gives the answer which is present value = $14,945.00 but no steps on how to get there. Thank you and have a nice day. This question came from an accounting business class online called The Kaplan E Guide to Business
Found 2 solutions by uma, venugopalramana:
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! When the present value is given, the future value is calculated using the formula:
FV = PV(i+r)^n
Here FV = 20000
r = 0.06
n = 5
==> 20000 = PV(1+0.06)^5
==> 20000 = PV(1.06)^5
==> 20000 = PV(1.3382)
==> 20000/1.3382 = PV
==> 14945.4 = PV
Thus the present value = $ 14945
Good Luck!!!
Answer by venugopalramana(3286)  (Show Source):
You can put this solution on YOUR website! Future Value the concept called Present value You want to buy a new car in 5 years and estimate you need $20,000.00.If the bank pays you 6% interest rate how much do you need to put in the bank today? I need step by step instructions of how to get the answer. The book gives the answer which is present value = $14,945.00 but no steps on how to get there. Thank you and have a nice day. This question came from an accounting business class online called The Kaplan E Guide to Business
I AM NOT SURE WHETHER YOU ARE AT HOME WITH ALGEBRA.ANY WAY I AM NOT USING X SYMBOL AND TRYING TO SHOW YOU A STANDARD BASE METHOD
LET US ASSUME YOU PUT 100 $ TO DAY
THE RATE OF INTEREST = 6%
YOU HAVE NOT MENTIONED WHETHER THE INTEREST IS COMPOUNDED EVERY YEAR OR NOT THAT IS WHETHER IT IS COMPOUND OR SIMPLE INTEREST.LET ME SHOW YOU BOTH VARIANTS.
VARIANT 1...........SIMPLE INTEREST..
THAT IS INTEREST IS NOT ADDED TO THE PRINCIPAL AT THE END OF THE YEAR, BUT PAID ONLY AT MATURITY CALCULATED ON THE ORIGINAL PRINCIPAL ONLY.
P=100.....R=6%=6/100..............T=5 YEARS
I = PTR=100*5*6/100=30
AMOUNT = P+I =130
SO IF YOU PUT 100 YOU GET 130 AT THE OF 5 YEARS.
HENCE IF WE WANT 20000, WE SHOULD PUT 20000*100/130=15384.8
VARIANT 2..........COMPOUND INTEREST.
THAT IS INTEREST IS ADDED TO THE PRINCIPAL AT THE END OF EVERY YEAR.
I YEAR
P=100.....R=6%=6/100..........T=1 YEAR
I=100*1*6/100=6
AMOUNT AFTER 1 YEAR = A1=100+6=106
II YEAR
P=106
I=106*1*6/100=6.36
A2=106+6.36=112.36
SIMILARLY
III YEAR
P3=112.96.....I3=6.74......A3=119.10
IV YEAR
P4=119.1......I4=7.15..........A4=126.25
V YEAR
P5=126.25.....I5=7.57..........A5=133.82
HENCE WE GET 133.82 AFTER 5 YEARS,IF WE PUT 100 AT THE BEGINING
HENCE TO GET 20000, WE SHOULD PUT 20000*100/133.82=14945.44
SINCE YOUR ANSWER TALLIES WITH COMPOUND INTEREST THIS YOU MAY TAKE AS THE CORRECT SOLUTION.
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If you want a formula then the formula is
A=P[1+R]^T.....where
P=principal...A=amount....R= rate of interest per rupee......T=time period in years
in our case
P=?...A=20000....R=6%=0.06.....T=5 years........hence
20000=P[(1+0.06)^5
P=20000/[1.06^5]=14945.44
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