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

Answer:

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

Answer 2

Answer:

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

$A=P\left(1+\frac{r}{n}\right)^{\left(nt\right)}$

$6000=5000\left(1+\frac{0.07}{12}\right)^{\left(12t\right)}$

$\frac{6000}{5000}=\left(1+0.00583333333333\right)^{\left(12t\right)}$

$1.2=\left(1.00583333333333\right)^{\left(12t\right)}$

$\ln\left(1.2\right)=12t\ ln[tex]\frac{\ln\left(1.2\right)}{12\ln\left(1.00583333333333\right)}=t$

\left(1.00583333333333\right)[/tex]

$2.61218303577=t$

Hence answer is approx 2.61 years.