You borrow $900 to buy a laptop. You plan to pay off the loan after 5 years of equal monthly payments. After 10 payments, you have $1200 left to pay. What is the simple annual interest rate of your loan?

The simple annual interest rate on my loan is 12%

Step-by-step explanation:

I planned to pay off the loan after 5 years of equal payments; There are 12 months that make up one year and the total number of months in five years = 12 × 5 = 60 months. This means that I planned to pay off the loan after 60 equal monthly payments.

If I have also made 10 of such monthly payments already and I have $1,200 left, it means that I now have 50 more months to clear the $1,200 that is left.

If I have $1,200 left to pay in 50 months, then my average payment per month is =

$1,200/50 = $24

Since I pay $24 monthly which includes part of the principal and the interest, then my total payment over the five years (60 months) will be = 24 × 60 = $1,440 (Principal+interest).

If the principal borrowed was $900, then the interest charged on the money over the 5 years = $1,440 - $900 = $540

With the interest known, we will now use the simple interest formula to find the simple annual interest rate on the loan.

Simple interest = (Principal×Rate×Time)/100

Where, S.I = $540

P = $900

T = 5years

R = ?%

540 = (900 × R × 5)/100

45R = 540

R = 540/45

R = 12%

Therefore, the simple annual interest rate on my loan is 12%

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)