SOLUTION: 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?

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.
------------
Investing $5000 instead of $10000 obviously requires less money. Is that better?

RELATED QUESTIONS
Which is the better deal, $10,000 invested at 5%, compounded yearly, for 20 years, or... (answered by lwsshak3)
Hello Tutors, Can I please have your assistance? Which is the better deal, $10,000... (answered by ikleyn,MathTherapy)
Hello tutor, please help me solve this. I tried and came up with the second one but I am... (answered by Boreal,solver91311)
If money is invested at r percent interest, compounded annually, the amount of the... (answered by Theo)
John invested R 10 000 at 6.75 for 3 years compounded annually (answered by ikleyn)
How much money should be invested at 5% compounded quarterly for 20 years so that you... (answered by ikleyn)
How much money should be invested at 5% compounded quarterly for 20 years so that you... (answered by ikleyn)
$900 invested at 5% for 10 years compounded... (answered by mananth)
Php 10, 000 is invested at 2% compounded annually. What is the exponential model for this (answered by ikleyn)