casey invested $1,225 in a certain bond that pays 19% interest compounded annually. How long will it take for Brad's investment to triple? Explain step by step.

6.32 years

Step-by-step explanation:

To get the time taken to triple the amount invested, we must first establish the compound interest formula. When a principal amount P is invested for a time n at a rate r percent, the amount A after n years may be expressed as

A = P (1 + r) ^n

Hence if $1,225 is to triple, the amount will be

= $1,225 * 3

= $3,675

The time n for this to happen may be computed through the equation

$3,675 = $1,225 (1 + 0.19) ^n

3 = 1.19^n

take the log of both sides

log 3 = log 1.19^n

using the law of logarithms that log a^b = b log a

n log 1.19 = log 3

n = log 3 / log 1.19

n = 6.32 years