Question

1) Sally needs $20,000 in 4 years. She has $10,000 to invest. If interest is compounded continuously, what rate is required for Sally to meet her goal?

Answer 1

Answer:

$17.33\%$

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  

$t=4\ years\\ A=\ 20,000\\ P=\ 10,000$  

substitute in the formula above  and solve for r

$20,000=10,000(e)^{4r}$

$2=(e)^{4r}$

Applying ln both sides

$ln(2)=4rln(e)$

$ln(2)=4r$

$r=ln(2)/4=0.1733$

Convert to percentage

$0.1733*100=17.33\%$