There are two different formulas:
The most common formula to use is:
F= IR^ t/p F: final amount I: initial amount R: rate of growth ( 5% = 0.05 +1 R>1) growth decay ( 5% R= 0.95) t: time p: time for R to occur (days, weeks, months,etc)
* note: t and p must be in same units
The second formula is for continuous interest rates:
P= Po e^ Kt P: final amount Po: initial amount e: calculator function K: growth/decay (no 1)
t: time
Example 1:
What will $3500 grow to, if invested at 6% interest for 10 years, compounded annually?
F= IR ^ t/p F=? I= 3500 R= 1.06 t= 10 p=1
(*note: if p is a fraction take the reciprocal and multiply it to the top number)
F= 3500(1.06)^10/1
F= 3500(1.06)^10
F= $6267.97
Example 2:
What amount of money would grow to $ 4000 if invested at 91/4%, compounded annually for 4 years?
F= IR ^ t/p F= 4000 I= ? R= 1.0925 t= 4 p=1
4000 = I (1.0925) ^ 4/ 1
(1.0925)^4 (1.0925)^4
I= $2807.85
Example 3:
In April. the atmosphere at Chernobyl was contaminated with radioactive iodine-131, which has a half-life of 8.1 days. How long did it take for the level of radiation to reduce to 1% of the level immediately after the accident?
*Half-life R= 0.5 P= half-life1/100 = 100(0.5)^t/8.1
0.01 = 0.5^t/8.1
log0.01 = t/8.1 log0.5
8.1 log0.01/log0.5 = t
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