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

Answer:

31 years to triple the investment

Step-by-step 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

$\frac{ln(3)}{0.035} = t$

t= 31.3889

Round to nearest whole number

t= 31 years