Question

Suppose we have an investment that earns interest compounded continuously, and it takes 12 years for an initial investment of $20,000 to grow to $60,000 under this investment. How long does it take for the same initial investment of $20,000 to grow to $80,000? (“ln” below denotes natural log with base “e”)

Answer 1

PV =20000
FV =60000
Time =12 Years
FV =PV*e^(r*t)
60000=20000*e^(r*12)
3 =e^(r*12)
Applying ln on both sides we get
ln3=r*12
Rate (r) =Ln(3)/12 =9.1151%

PV =20000
FV =80000
FV =PV*e^(r*t)
80000=20000*e^(9.1151%*t)
Applying ln on both sides
we t =ln(4)/9.1151% =15.14 years

Number of years =15.14