Respuesta :
It will take 2.612 years to get returns as $6000 over such investment at the interest rate of 7 percent per year.
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(1+\frac{r}{n} )^{nt}[/tex]
6000 = [tex]5000(1+\frac{0.07}{12} )^{12t}[/tex]
[tex]\frac{6000}{5000} = (1+0.00583333)^{12t}[/tex]
[tex]1.2= (1.00583333)^{12t}[/tex]
t = [tex]\frac{1.2}{12(1.0058333)}[/tex]
t = 2.61 years
So we can say that it takes 2.61 years to make such investment into $6000 at the interest rate of 7% which is compounded on a monthly basis.
Hence, The correct option is D is that it will take 2.612 years to get returns as $6000 over such investment at the interest rate of 7 percent per year.
Find out more information about interest rate here
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