Answer :
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
[tex]A=P\left(1+\frac{r}{n}\right)^{\left(nt\right)}[/tex]
[tex]6000=5000\left(1+\frac{0.07}{12}\right)^{\left(12t\right)}[/tex]
[tex]\frac{6000}{5000}=\left(1+0.00583333333333\right)^{\left(12t\right)}[/tex]
[tex]1.2=\left(1.00583333333333\right)^{\left(12t\right)}[/tex]
[tex]\ln\left(1.2\right)=12t\ ln[tex]\frac{\ln\left(1.2\right)}{12\ln\left(1.00583333333333\right)}=t[/tex]
\left(1.00583333333333\right)[/tex]
[tex]2.61218303577=t[/tex]
Hence answer is approx 2.61 years.
Answer:
2.61 years is how long it would take until you have $6,000 without depositing and additional funds.