You put $1700 into an account at 8% per year compounded continuously.

a) How long will it be until you have $2000?
b) What is the doubling time for this money?

2000 = 1700 e^.08x

x = 2.03

for doubling,
2=e^.08x
x = 8.67
agrees with rule of 72

To find the answers to these questions, we can use the formula for continuous compound interest:

A = P * e^(rt)

where:
A = the final amount
P = the principal amount (initial investment)
e = Euler's number, approximately 2.71828
r = annual interest rate (as a decimal)
t = time in years

Let's use this formula to solve the two parts of the question:

a) How long will it be until you have $2000?

We can rearrange the formula to solve for time (t):

t = ln(A/P) / r

where ln is the natural logarithm.

Substituting the given values:
A = $2000, P = $1700, and r = 8% = 0.08, we can calculate t:

t = ln(2000/1700) / 0.08

Using a calculator, we get:

t ≈ 0.0648 years

Since time is typically measured in years, we can convert 0.0648 years to months or days if needed.

b) What is the doubling time for this money?

In this case, we need to find the time it takes for the investment to double, which means the final amount (A) is twice the initial amount (P). So:

A = 2P

We can use the same formula as before and solve for time (t):

t = ln(A/P) / r

Substituting A = 2P = 2 * $1700, P = $1700, and r = 8% = 0.08, we can calculate t:

t = ln((2 * 1700) / 1700) / 0.08

Using a calculator, we get:

t ≈ 0.0866 years

Again, if needed, we can convert 0.0866 years to months or days.