How long will it take money to triple if it is invested at a

How long will it take money to triple if it is invested at

a) 7% compounded daily

b) 7.3% compunded continuously

( round to 2 decimal places as needed)

Solution

Compound interest formula for daily compounding:
A=P(1+r)^n, P=initial investment, r=interest rate per period, n=number of periods, A=amt after n periods.
For given problem:
A=P(1+r)^n
A/P=(1+r)^n=3
(1+.07/365)^n=3
(1+.000192)^n=3
(1.000192)^n=3
take log of both sides
nlog(1.000192)=log3

n=5729days or 15.7 years

b)

Compound interest formula for continuous compounding:
A=Pe^rt, P=initial investment, r=interest rate per year, t=number of years, A=amt after t years.
A/P=e^rt=3
e^.073t=3
take log of both sides
.073t*lne=ln3
lne=1

.073t=ln3
t=ln3/.07315.05 yrs