Question

how long will it take an investment of $300 to triple, if the interest rate is 3.5% per year, compounded continuously?

Answer 1

31 years to triple the investment

Explanation:

Initial investment = 300

Triple amount that is final amount = 300*3= 900

rate of interest = 3.5 % = 0.035

we need to find out number of years (t)

for compounded continuously we use formula

`A= Pe^(rt)`

A is the final amount

P is the initial amount

r is the rate of interest

t is the number of years

`900 = 300e^(0.035*t)`

Divide both sides by 300

`3 =e^(0.035*t)`

take 'ln' on both sides

`ln(3) =ln(e^(0.035*t))`

ln(3) = 0.035t ln(e)

ln(e)= 1

`(ln(3))/(0.035) = t`

t= 31.3889

Round to nearest whole number

t= 31 years