TVM Samples
Time Value of Money Formula:
FV = PV(1+i)^n
Link to Financial Calculators by Bishinew Incorporated
Future Values
Example FV01:
How much will $10,000 be in 10 years time and have an annualized returns of 7%?
PV = $10,000
i = 7%
n = 10 years
Answer: FV = $19,671.51
Note: The negative value shows the opposite of initial value. Eg. If you deposit $10,000 you will able to withdraw -$19,671.51.
Example FV02:
How much will $10,000 be in 5 years time and with annual rate of returns of 8%?
PV = $10,000
i = 8%
n = 5 years
Answer: FV = $14,693.28
Example FV03:
How much will $500 monthly investments (starting now) will be in 20 years time and with annual rate of returns of 8%?
PMT = $500
i = 8%
n = 240 months (20 years)
Compounding = Monthly
Mode: Beginning
Answer: FV = $296,473.61
Example FV04:
How much will $500 monthly investments (starting end of the month) will be in 20 years time and with annual rate of returns of 8%?
PMT = $500
i = 8%
n = 240 months (20 years)
Compounding = Monthly
Mode: End
Answer: FV = $294,510.21
Example FV05:
How much will initial $1,000 and monthly $200 be in 20 years time and with annual rate of returns of 8%?
PV = $1,000
PMT = $200
Annual rate, i = 8%
Periods, n = 240 months (20 years)
Mode: End
Answer: FV = $122,730.89
Present Values
Example PV01:
How much to invest now to get $10,000 in 10 years time and have an annualized returns of 7%?
FV = $10,000
i = 7%
n = 10 years
Answer: PV = $5,083.49
Example PV02:
How to get $10,000 in 5 years time and with annual rate of returns at 8%? How much to save now?
FV = $10,000
i = 8%
n = 5 years
Answer: PV = $6,805.83
Payments
Example PMT01:
How much to invest yearly starting now to get $10,000 in 5 years time and have an annualized returns of 8%?
FV = $10,000
i = 8%
n = 5 years
Mode: Beginning
Answer: PMT = $1,578.30
Example PMT02:
How much to invest yearly starting at the end of the year, to get $10,000 in 5 years time and have an annualized returns of 8%?
FV = $10,000
i = 8%
n = 5 years
Mode: End
Answer: PMT = $1,704.56
Example PMT03:
I want to invest $50,000 now. How much to invest monthly starting now, to get $1,000,000 in 25 years time and with an annualized returns of 8%?
PV = $50,000
FV = $1,000,000
i = 8%
n = 300 months (25 years)
Compounding: Monthly
Mode: Beginning
Answer: PMT = $1,427.88 per month
Example PMT04:
How much monthly withdrawal for 20 years (withdraw at the end of the month) will you get if you invest $500,000 now? Your investment will still give annualized returns of 8% per annum.
FV = $500,000
i = 8% p.a.
n = 240 months (20 years)
Compounding = Monthly
Mode: End
Answer: PMT = $4,182.20 monthly withdrawal
Return Rate, I
Example I01:
What is the required yearly return rate for $500 yearly investments at the beginning of the years to get $10,000 in 10 years.
FV = $10,000
PMT = -$500 yearly
n = 10 years
Mode: Beginning
Answer: i= 12.304% yearly
Note: Remember to add negative sign at the payments to show you pay out the yearly amount.
Example I02:
What is the required yearly return rate for $500 yearly investments at the end of the years to get $10,000 in 10 years.
FV = $10,000
PMT = -$500 yearly
n = 10 years
Mode: End
Answer: i= 14.691% yearly
Note: Remember to add negative sign at the payments to show you pay out the yearly amount.
Periods
Example N01:
How many $500 yearly investments at the beginning of the years to get $10,000 and with an annualized returns of 8%?
FV = $10,000
i = 8%
PMT = $500 yearly
Mode: Beginning
Answer: N= 11.81 times (years)
Example N02:
How many $500 yearly investments at the end of the years to get $10,000 and with an annualized returns of 8%?
FV = $10,000
i = 8%
PMT = $500 yearly
Mode: End
Answer: N= 12.42 times (years)
Cost of Procrastination
Example CP01:
Ali and Andrew are good friends and are of the same age. Ali started investing $200 per month at age 25. Andrew started investing $200 per month at age 35. Both invested for 10 years only. What are the amounts accumulated at age 55? What is the amount difference between Ali & Andrew? Assume annualized returns of 8%.
Ali Step 1 : Age 25 to 35
i = 8%
PMT = $200 monthly
Mode: Beginning
n = 120 months (10 years)
Compounding: Monthly
After 10 years, FV = $36,833.14
Ali Step 2 : Age 35 to 55
i = 8%
PV = $36,833.14
Mode: Beginning
n = 20 years
Compounding: Annually
After next 20 years, FV = $171,677.69
Andrew Step 1 : Age 35 to 45
i = 8%
PMT = $200 monthly
Mode: Beginning
n = 120 months (10 years)
Compounding: Monthly
After 10 years, FV = $36,833.14 (Note: Same as Ali)
Andre Step 2 : Age 45 to 55
i = 8%
PV = $36,833.14
Mode: Beginning
n = 10 years
Compounding: Annually
After next 10 years, FV = $79,519.99
The difference = $171,677.69 - $79,519.99 = $92,157.70
Ali took advantage of 10 more years to accumulate his investments.
Conclusion: Start investing early and use the power of compounding and longer time in the investments.
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