Question

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

that pays 14% interest compounded
continuously. How long will it take
Brad's investment to triple?

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* \$ 2300=\$ 6900`

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

`6900=2300e^(0.14t)`

`(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]`

`(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.