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Sladkaya [172]
3 years ago
12

Your bank account is sitting on $14,000. You started with a principal balance of $12,500. If the interest rate was 4.5% compound

ed continuously, how long was your money in the bank?
Mathematics
1 answer:
Simora [160]3 years ago
3 0

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  

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