How long will it take $5,000 to grow to $17,000 if it is invested at 4% compounded monthly

Question

Find the amount in years, rounded to the nearest tenth of a year.

Answer 1

Hi,

the formula for compounded interest is A=A₀+A₀^nrt

we are given: A=$17,000 , A₀=$5000 , n=12 , r=0.04

we want to find t.

1. we can make this formula easier by dividing the dollar amount by 1000 (since they are just a factor of 1000, they wont affect the time it take to grow the money). Then A=17 and A₀=5
2. next we plug into the formula: 17=5+5^12*0.04*t
3. evaluate: 12=5^0.48*t becomes logbase5 of(12) =0.48t then (logbase5 of (12) / 0.48)=t so t=3.2 years or 3 years and about 2 months and 1 week