Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily, and continuously. (Round your answers to two decimal places.)

Question

r= 4.3%

(a) annually

(b) monthly

(c) daily

(d) continuously

Answer 1

2 = e^rt for continuous compounding

2 =e^.043t

take natural logs

ln2 = .043t

t = ln2/.043 = about 16.12 years to double your investment

for annual compounding

2 = (1.043)^t

take logs to the base 1.043

log_1.0432 = t

t = ln2/ln1.043 = 16.66 years to double the investment

for monthly compounding

2 = (1+.043/12)^12t

2= (1.00358333...)^12t

t = ln2/ln1.033358333../12

t = 16.15 years to double the investment

for daily compounding

2 = (1+.043/365.25)^365.25t

2=(1.0001177275838)^365.25t

t = ln2/ln1.0001177275838/365.25

t = 16.12 years to double investment

use base change of logs to natural logs if that's easier for your calculator