Question

Jacobs college savings are invested in a bond that pays an annual interest of 6.2% compounded continuously. How long will it take for the money to triple

Answer 1

Answer:

Therefore the value of bond will triple after 17.72 years.

Step-by-step explanation:

The formula of Compounded continuously

$A=Pe^{rt}$

A= Amount after t year

P= initial amount

r = rate of interest

t= time in year.

Given that,

Jacobs college saving are invested in bond that pay 6.2% compounded continuously.

Let after t years the initial amount P will be triple i.e 3P.

Here P=P, A=3P, r= 6.2%=0.062

$\therefore 3P=Pe^{0.062t}$

$\Rightarrow 3=e^{0.062t}$   [ Multiply $\frac 1P$ both sides]

Taking ln both sides

$\Rightarrow ln3=ln(e^{0.062t})$

$\Rightarrow ln3={0.062t}$        [ since $ln(e^a)=a$ ]

$\Rightarrow t=\frac{ln3}{0.062}$

$\Rightarrow t\approx 17.72$ years

Therefore the value of bond will triple after 17.72 years.