Question

Suppose that $1500 is initially invested in an account at a fixed interest rate, compounded continuously. Suppose also that, after two years, the amount of money in the account is $1577 . Find the interest rate per year.


Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

Answer 1

You could say fter 2 years this formula has been used 1500 * (1. n )^2 = 1577 where n is the interest rate as a decimal and 1.n is the initial sum plus interest rate. Of course ^2 means the power has been raised by the number of years interest has been added.
All you do now is divide both sides by 1500 giving...
(1.n)^2 = 1.0513333...
Now take the square root of both sides
1.n =1.02534547
So n = 0.02534547
But remember this is a decimal version, so simply multiply by 100 to get the percentage rate of interest.
100 *0.02534547 = 2.534547%

Answer = 2.534547% interest