Suppose that you have an investment....

Question

Suppose that you have an investment that earns 0% in the first year, 10% in the second yea

a. what rate of interest, compound annually, would yield the same return after two years?

b. what rate of interest, compounded continuously, would yield the same return after two years?

Answer 1

a)

A = P * (1 + (r/n))^(n*t)

where:
A is current amount

P is principle (initial) amount
r is rate of interest
n is compound frequency, here 1
t is time, 2

b)

 

A = P * e^(r*t)

where,
A is current amount
P is principle (initial) amount
r is the rate of interest
t is the time in years, here 2

 

in both cases, A/P would be 1.1 which is the 10% earned in the scenario initially stated which you are to compare with.  If you take the natural log of both sides of the equations, then you can solve for r in each part.