Sarah and azhar both invest $10,000. sarah invests her $10,000 at a rate of x% compound interest per year. azhar invests his $10,000 in a bank that pays 2% simple interest per year. after 7 years, their investments are worth the same amount. calculate the value of x.

The firts thing we are going to do here is use the simple interest formula: 
where 
is the final amount after  years
is the initial investment  
is the interest rate in decimal form 
is the number of years 
With this formula we will find the final amount Azhar's investment after 7 years. We know from our problem that , , and . Lets replace those values in our formula to find :




Now, since Sarah is investing in a compound interest account, we are going to use the compound interest formula: 
where
is the final amount after  years
is the initial investment 
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the number of years
Notice that we know from our problem that after 7 years their investments are worth the same amount, so . We also know that , , and . Since the interest are compounded per year, . Lets replace all the vales in our compound interest formula and solve for  to find our rate:








We can conclude that the interest rate of Sarah's investment is approximately 1.89%, so x=1.89%.