if you compound continously $20,000.00 at 8 % interest how long will it take to double the money
2007-01-23 01:13:07 · 5 answers · asked by brian_0680 2 in Science & Mathematics ➔ Mathematics
How about a definite formula for continuous compounding:
FV = P*(1+r/n)^(nt)
FV = Future Value
P: Principal invested
r: ANNUAL interest rate
n: number of compounding periods
t: number of years you choose to invest
So, for continuous compound interest, n-->∞
FV = limit (n-->∞)P*(1+r/n)^(nt)
let k=n/r
FV = limit (k-->∞)P*(1+1/k)^(krt) = P* limit (k-->∞){(1+1/k)^k}^rt
Now, you have to recognize that limit (k-->∞){(1+1/k)^k} = e (natural logarithm base).
So: for continuous compounding: FV=P*e^rt
For your problem, we have to solve for t:
t = 1/r* ln|FV/P| = 1/.08 * ln|40000/20000| = 1/.08*ln|2| = 8.66 years.
2007-01-23 01:57:57 · answer #1 · answered by mjatthebeeb 3 · 0⤊ 0⤋
About 9 years. See how well that works? Preykill probably spent 5 minutes on those calculations.
By the Rule of 72, divide 72 by the rate of return and you will get how long it takes to double.
2007-01-23 09:24:35 · answer #2 · answered by gebobs 6 · 1⤊ 0⤋
$20.000,00
year 1 $21.600,00
year 2 $23.328,00
year 3 $25.194,24
year 4 $27.209,78
year 5 $29.386,56
year 6 $31.737,49
year 7 $34.276,49
year 8 $37.018,60
year 9 $39.980,09
year 10 $43.178,50
any help? should take a bit more then 9 years!
2007-01-23 09:23:46 · answer #3 · answered by Preykill 5 · 1⤊ 0⤋
20000x8%=1600,,,,,,,,37015x8.=2961
21600X8%=1728,,,,,,,,39976 end...Ä°t is TEN years.
23328x8.=1866
25194x8.=2015
27209x8.=2176
29385x8.=2350
31735x8.=2538
34273x8.=2742
2007-01-23 09:36:19 · answer #4 · answered by Tuncay U 6 · 0⤊ 0⤋
according to my calculations... 12.5 years.
2007-01-23 09:38:49 · answer #5 · answered by Anonymous · 0⤊ 0⤋