SOLUTION: Victoria invests $1500 in an account that earns 3% interest annually. her friend James invests $1200 in an account that earns 3% interest annually compounded continuously. how long

Question 1009996: Victoria invests $1500 in an account that earns 3% interest annually. her friend James invests $1200 in an account that earns 3% interest annually compounded continuously. how long will it take for their two accounts to become equal in value. will this likely occur during their lifetimes?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the future value of 1500 at 3% interest compounded annually for 100 years is:

f = 1500 * 1.03^100 = 28828 rounded to the nearest dollar.

the future value of 1200 at 3% interest compounded continuously for 100 years is:

f = 1200 * e^(.03*100) = 24103

in fact, they initially get further apart and then come closer to each other relatively quickly until they become the same at between 505 and 506 years out.

the following graph shows that relationship.

$$$

the difference grows to 25 million or so around the 475th year and then dramatically closes to 0 around the 505th year.

the graphed equation is 1500 * 1.03^x - 1200 * e^(.03x).

you are looking for when the value of that equation equals 0.

that equation was derived from 1500 * 1.03^x = 1200 * e^(.03x).

all that was done was subtracting the expression on the right side of the equation from both sides of the equation.

if they are equal, then if you subtract one from the other, the result should be 0.

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