Question

A woman invests $5800 in an account that pays 6% interest per year, compounded continuously.

Answer 1

Answer:

Part a) $\ 6,539.48$  

Part b) $5.36\ years$  

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

Part a) What is the amount after 2 years?

we have  

$t=2\ years\\ P=\ 5,800\\ r=0.06$  

substitute in the formula above  

$A=\ 5,800(e)^{0.06*2}=\ 6,539.48$  

Part b) How long will it take for the amount to be $8000?

we have  

$t=?\ years\\ P=\ 5,800\\ r=0.06\\A=\ 8,000$  

substitute in the formula above  and solve for t

$\ 8,000=\ 5,800(e)^{0.06t}$  

$(8,000/5,800)=(e)^{0.06t}$  

Applying ln both sides

Remember that

ln(e)=1

$ln(8,000/5,800)=0.06t$  

$t=ln(8,000/5,800)/0.06=5.36\ years$