Question

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?

Answer 1

2.61 years is how long it would take until you have $6,000 without depositing and additional funds.

Answer 2

Approx 2.61 years.

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

`A=P\left(1+(r)/(n)\right)^(\left(nt\right))`

`6000=5000\left(1+(0.07)/(12)\right)^(\left(12t\right))`

`(6000)/(5000)=\left(1+0.00583333333333\right)^(\left(12t\right))`

`1.2=\left(1.00583333333333\right)^(\left(12t\right))`

`\ln\left(1.2\right)=12t\ ln[tex](\ln\left(1.2\right))/(12\ln\left(1.00583333333333\right))=t`

\left(1.00583333333333\right)[/tex]

`2.61218303577=t`

Hence answer is approx 2.61 years.