Tom invests $10,000 in a savings account that offers 3.5 percent interest, compounded continuously. in 10 years tom will have earned $(blank) in interest, and in (blank) years the investment will double. (use the rule of 70 where required.)

Compound  interest  formula

 

Where

A= Future value
P = the Principal (the initial amount of money) 
r = annual interest rate

t = time

n= number of times compounded in one t

Remark
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r is generally a percentage like 3%, 7% etc and are applied in the formula as 0.03, 0.07..., 

the interest is compounded generally annually (n=1), quarterly (n=4), monthly (n=12), etc...

t is in years,

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Compounding continuously means that n tends (or goes) to infinity.

As n goes to infinity, the expression  is:



where e = 2.718.... (I assume this is rule 70)
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In short, when n is infinite, that is when we compound continuously, the formula is :

, 

for P=$10,000, r=3.5/100=0.035, and t=10 years, we have:



dollars.

To perform the last equation we make use of a scientific calculator.

$14,190.7

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