You decide to put $100 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% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?

170.202 years

Step-by-step explanation:

From the compound interest formula, that has interest rate in times per year but compounds monthly we have

A is the amount you want to save, P is the principal (what you put down, in this case 100), r is the anual interest rate, n is 12 i.e the times it compounds, and t is the amount of years it will take. So we have data for all variables but t.

Solving for t we have

taking logs

finally

replacing and calculating we get t=170.202

$79500

step-by-step explanation: