Raymond B. answered • 12/14/22
Tutor
5
(2)
Math, microeconomics or criminal justice
doubling time = 12 years
Amount after 10 years = A = 2000
2 = e^12r where r= annual interest rate
take natural logs of both sides
ln2 = 12r
r = (ln2)/12= about 0.05776 = 5.776% interest rate
in 10 years
A = Pe^10(ln2)/12
A= Pe^.5776 = about 1.7818P = 2000
P = 2000/1.7818 = $1122.49 = initial investment
in 12 years
A = Pe^ln2 = 2P= 2244.98
in zero years
A = P = Pe^0 = P(1)= 1122.49
General formula is
A =Pe^rt for continuous compounded interest
where
P= initial investment
r = annual interest rate
t = number of years
e = an irrational number = about 2.71828...
A= ending Amount after t years at r interest rate, with P initial investment
