In this lesson 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 - goes down 5) 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 only used 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 monthly?
F= IR ^ t/p F=? I= 3500 R= 1.005 t= 10 p=1/12
(*note: if p is a fraction take the reciprocal and multiply it to the top number)
F= 3500(1.005)^10/(1/12)
F= 3500(1.005)^120
F= $6367.88
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:
P= 100(0.87)^n represents the percent of caffeine in your body n hours after consumption. Write this equation as an exponential function with 1/2 as the base instead of 0.87
R= 0.87 (down) 13% per hr
0.5 = 0.87^ t
log0.5 = t log0.87 1) log both sides
log0.87 log0.87
5 = t
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