SOLUTION: You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long

Question 979641: You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
3000=150{1+(0.025/12)}^12t ; t=years. divide the interest by the number of compoundings per year and raise it to the number of years * 12 months/year.
As a note, this has to double more than 4 times, and the rule of 72 for doubling, which can loosely be used for this, suggests that doubling will take 29 years. This will take somewhere in the neighborhood of 120-140 years.
20={1+0.002083}^12t
ln of both sides
ln 20= 12t ln (1.002083)
2.9957=12 t *(0.002080)
without rounding yet
do ln20/(12*0.002080) =t
t=119.973 years.

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