logarithmic

Question

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

Answer 1

If it earns 0.45% each month then each month it is 1.0045 times the previous month's balance

 

F_v = F₀(1.0045)^m   where F_v is future value, F₀ is beginning value, and m is number of months

 

1124 = 1000(1.0045)^m

 

1124/1000 = 1.0045^m

Take log of both sides

 

log(1124/1000) = m[log 1.0045]

 

m = [log(1124/1000)]/(log 1.0045)

 

m = 26.035 months

 

It will take 26 months or 2 years 2 months to reach a balance of $1124