Question

Your bank account is sitting on $14,000. You started with a principal balance of $12,500. If the interest rate was 4.5% compounded continuously, how long was your money in the bank?

Answer 1

Answer:

$t=2.5\ years$  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

$t=?\ years\\ P=\ 12,500\\P=\ 14,000\\ r=4.5\%=4.5/100=0.045$  

substitute in the formula above   and solve for t

$14,000=12,500(e)^{0.045t}$  

Simplify

$14,000/12,500=(e)^{0.045t}$  

$1.12=(e)^{0.045t}$  

Apply ln both sides

$ln(1.12)=ln[(e)^{0.045t}]$  

$ln(1.12)=(0.045t)ln(e)$  

Remember that

$ln(e)=1$  

so

$ln(1.12)=(0.045t)$  

$t=ln(1.12)/(0.045)$  

$t=2.5\ years$