Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)

Question

Initial Investment: $600

Amount after 10 years: $1805

Interest Rate: ?

Amount of time it takes to double: ?

Answer 1

the underlying formula that you want to use to set this one up for continuous compounding is

A = P*e^(rt)

for this scenario that means taking

r = ln(A/P) / t

r = ln(1805/600) / 10

r = 1.1014 / 10 = 0.11014, meaning that the interest rate here is 11.01%

to find the doubling time then you want to use the formula t_double = ln(2) / r)

t_double = ln(2) / 0.11014

t_double = 6.293

meaning that it will take about 6.29 years for the amount of the investment to double

Answer 2

We need the formula for continuously compounded interest here: FV = Pe^rt (FV for future value, P for principal, r for rate, t for time in years). We need to solve for both of the variables in the exponents, so we'll need logarithms.

We can first solve for r:

1805 = 600 e^r*10

(1805/600) = e^r*10

ln(1805/600) = ln(e^r*10)

ln(1805/600) = r*10

[ln(1805/600)/10] = r

0.1101 ≈ r

As a percentage: 11.01%

Then we can find doubling time, where FV = 1200:

1200 = 600e^0.1101*t

2=e^0.1101*t

ln(2) = ln(e^0.1101*t)

ln(2) = 0.1101*t

[ln(2)/0.1101] = t

6.30 ≈ t