Determine how long it takes until the two investments have the same value

Question

Investment A is currently worth $80,000 and is growing at a rate of 7% per year compounded continuously. Investment B is currently worth $70,000 and is growing at a rate of 10% per year compounded quarterly. Determine how long it takes until the two investments have the same value

Answer 1

80K at 7% compounded continuously

A = 80e^.07t where t = years

A = 70(1+ .1/4)^4t = 70(1.025)^4t

set them equal

80e^.07t = 70(1.025)^4t

solve for t