Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.)
Initial Investment:
Annual % Rate:
Time to Double: 8 yr
Amount After 10 Years: $1700
I don't understand how to get in the initial investment of annual % rate given only the time to double and amount after 10 years.
to double in 8 years, you need interest rate r where
(1+r)^8 = 2
r = 0.0905 or 9.05%
So, with initial amount P, you have
P(1+.0905)^10 = 1700
Now just solve for P.
Steve your calculations/formulas are wrong they do not work for continuous compounding sorry
STEVE YOU THE MAN! THANK YOU!
To find the initial investment and annual interest rate, we can use the formula for continuously compounded interest:
A = P*e^(r*t)
Where:
A = Amount after time t
P = Initial investment
r = Annual interest rate
t = Time in years
e = The base of the natural logarithm, approximately 2.71828.
Given that the time to double is 8 years, we can find the annual interest rate using the formula:
2P = P*e^(r*8)
Simplifying the equation, we get:
2 = e^(8r)
Taking the natural logarithm of both sides:
ln(2) = 8r*ln(e)
Since ln(e) is equal to 1, the equation simplifies to:
ln(2) = 8r
Solving for r, we divide both sides of the equation by 8:
r = ln(2)/8
Now we can calculate the initial investment (P). Given that the amount after 10 years is $1700, we use the formula:
$1700 = P*e^(r*10)
Substituting the value of r we found earlier, we get:
$1700 = P*e^((ln(2)/8)*10)
Simplifying the equation:
$1700 = P*e^(ln(2)*(10/8))
Since e^(ln(2)) is equal to 2, the equation further simplifies to:
$1700 = P*2^(10/8)
To solve for P, divide both sides of the equation by 2^(10/8):
P = $1700 / 2^(10/8)
Calculating this expression, we find the initial investment (P) rounded to two decimal places.