Predicting Change

Question

Suppose $12,200 is invested in an annually compounded account at 4.64%. Approximately how long will it take for the balance to reach $33,550?

Answer 1

 

 12200 (1.0464)^t = 33550

 

 1.0464^t = 33550/12200

 

After taking the log of both sides the t

moves in front, by property of logarithms.

 

The equation becomes:

 

t* log(1.0464) = log(33550/12200)

 

                      = log 33550 - log 12200 <--- another property of logarithms

 

t = ( log 33550 - log 12200 )/log(1.0464)

 

 = 22.303720884

 

  22 years 3 months 4 days 12 hours 18 minutes 5 seconds

 

 

Answer 2

P(t) = P₀·(1 + r)^t

• P(t) = Principle at time t = $33,500
• P₀ = starting principle = $12,000
• r == rate expressed as a decimal = 4.64% = 0.0464
• t = time (years)

 

P(t) = P₀·(1 + r)t

33,550 = 12,200·(1 + 0.0464)^t

33,550 = 12,200·(1.0464)^t

2.75 = (1.0464)^t

log(2.75) = t·log(1.0464)     [Log property: log(a^b) = b·log(a)]

log(2.75)/log(1.0464) = t

 

Use your calculator to compute the answer.  You can use any base log.  The answer is in years.