Question 1141093: Which is the better deal, $10,000 invested at 5%, compounded yearly, for 20 years, or $5,000 invested at 10%, compounded continuously, for 20 years?
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! for discrete compounding, the formula is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods
with your inputs, you get:
f = what you want to find
p = 10,000
r = 5% per year / 100 = .05 per year.
n = 20 years
formula becomes:
f = 10,000 * (1 + .05) ^ 20
solve for f to get f = 26,532.97705
for continuous compounding, the formula is f = p * e ^ (r * t)
f is the future value
p is the present value
e is the scientific constant equal to 2.718281828.....
r is the interest rate per time period.
t is the number of time periods
with your inputs, you get:
f = what you want to find.
p = 5,000
r = 10% / 100 = .10
t = 20 years
formula becomes:
f = 5,000 * e ^ (.10 * 20)
solve for f to get f = 36,945.28049.
looks like continuous compounding at 10% winds over discrete compounding at 5%, even when the initial investment for continuous compounding at 10% per year is half the initial investment for discrete compounding at 5% per year.
you can graph both equations.
this is what it looks like.
the graph shows that the two investments break even at about 13 and a half years out.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! "better" is not a clearly defined term.
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Investing $5000 instead of $10000 obviously requires less money. Is that better?
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