Question

1. Brad invested $2,300 in a corporate bond

Answer 1

Given:

Principal value = $2300

Rate of interest = 14% compounded continuously.

To find:

The time taken by Brad's investment to triple.

Solution:

The formula for amount after the compound interest (Continuously) is:

$A=Pe^{rt}$

Where, P is the principal, r is the rate of interest in decimal and t is the time period.

Triple of Brad's investment is

$3\times \ 2300=\ 6900$

Substituting $A=6900,P=2300\ r=0.14$, we get

$6900=2300e^{0.14t}$

$\dfrac{6900}{2300}=e^{0.14t}$

$3=e^{0.14t}$

Taking natural log on both sides, we get

$\ln 3=\ln e^{0.14t}$

$1.0986=0.14t$                $[\because \ln e^x=x]$

$\dfrac{1.0986}{0.14}=t$

$7.84714=t$

After approximating the value, we get

$t\approx 7.85$

Therefore, Brad's investment will take 7.85 years to triple.