Question

Suppose that $1,000 is invested at 5% interest compounded continuously. Use the formula

A = Pert.
(a) How long (to the nearest day) before the value is $1,250?
years,
days

(b) How long (to the nearest day) before the money doubles?
years,
days

(c) What is the interest rate (compounded continuously and rounded to the nearest tenth of a percent) if the money doubles in 5 years?
%

Answer 1

(a)

`1000 {e}^(.05t) = 1250`

`{e}^(.05t) = (5)/(4)`

`.05t = ln(5) - 2 ln(2)`

`t = 20 ln(5) - 40 ln(2) = 4.46 \: years`

4.46 years = 4 years, 167.9 days

(b)

`1000 {e}^(.05t) = 2000`

`{e}^(.05t) = 2`

`.05t = ln(2)`

`t = 20 ln(2) = 13.86 \: years`

13.86 years = 13 years, 313.9 days

(c)

`1000 {e}^(5r) = 2000`

`{e}^(5r) = 2`

`5r = ln(2)`

`r = (1)/(5) ln(2) = .1386 = 13.86\%`