Question 996347
Alice invests $5000 at Bob's bank and $8000 at Charlie's bank. Bob compounds interest continuously at a nominal rate of 10%. Charlie compounds interest continuously at a nominal rate of 7%. 
A). In how many years will the two investments be worth the same amount?
Bob's interest:: 5000*e^(0.10t)
Charlie's interest:: 8000*e^(0.07t)
Solve:: 5000e^(0.10t) = 8000e^(0.07t)
e^(0.03t) = 8/5
0.03t = ln(8/5)
-----
t = (100/3)*0.47
t = 47/3
t = 12 1/3 years
=======================
 
B). When both investments are worth the same amount, 
how much will each be worth?
5000e^(0.1*(47/3)) = $21293.21
-----
Cheers,
Stan H.
---------