logarithmic

Question

you start a savings account with $1000. this account earns 0.45% per month. When will it reach $1124?

Answer 1

A(t) = A₀(1 + rate)^t

• A(t) = amount of money at month t = $1124
• A₀ = starting amount = $1000
• rate = rate expressed in decimal form = 0.45% = 0.0045
• t = months

 

A(t) = A₀(1 + rate)^t

$1124 = $1000(1+0.0045)^t

1124/1000 = (1.0045)^t

1.124 = (1.000045)^t

log(1.124) = log(1.0045^t)

log(1.124) = t·log(1.0045)       [Log Property: log(a^b) = b·log(a)]

log(1.124)/log(1.0045) = t

 

Use your calculator to get the answer.  You can use any base log.