Question

Phineas invests $2,000 at a nominal annual interest rate of 4% compounded semi annually.
Ferb invests $2,500 at an effective annual rate of 3%. Candace can earn an effective annual interest
rate of 6%. How much should Candace invest so that there is a point in time in the future where
all 3 have the exact same dollar amount at the exact same time? Hint: First find when Phineas and
Ferb have the same balance.

Answer 1

Calculating the time at which the compounded amount invested by Phineas and Ferb are the same.

Compounded amount of Phineas investment = 2000*(1+0.04/2)^(2*n) {Where as n = number of the year at which the compounded amount will be equal for both siblings}

Compounded amount of Ferb investment = 2500*(1+0.03)^(n)

Equating the above two equation we get, n = 22.21117898

{we would get something like 1.010097087^n = 1.25; after that we would take log to find the value of 'n'}

Now we find the amount Candace should invest @ 6% annually so that at the time 22.21117898 year she would also have same amount as that of her other two siblings.

Lets take x= invested amount by Candace, equating this with the Ferb compounding value,

2500*(1+0.03)^(22.21117898) = x*(1.06)^22.21117898

By solving above equation we get, x= $1,321.28