You decide to put $5,000 in a savings account to save for a $6,000 downpayment on a new car. if the account has an interest rate of 7% per year and is compounded monthly, how long does it take until you have $6,000 without depositing any additional funds?

Approx 2.61 years.

Step-by-step explanation:

Given that you decide to put $5,000 in a savings account to save for a $6,000 down payment on a new car.

That means A=6000 and P=5000

If the account has an interest rate of 7% per year and is compounded monthly,

Then r=7%= 0.07 and n=12 (monthly)

Now we need to find about how long does it take until you have $6,000 without depositing any additional funds.

So let's plug these values into compound interest formula and fine time t

\left(1.00583333333333\right)" alt="\frac{\ln\left(1.2\right)}{12\ln\left(1.00583333333333\right)}=t" />

\left(1.00583333333333\right)" />

Hence answer is approx 2.61 years.

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step-by-step explanation: