Reagan has a savings account that earns 1.87% interest, compounded quarterly. if she needs $20,857 for a down payment on a house in 9 years, how much money will she need to invest in the account today? a. 10,704.95 b. 17,633.17 c. 19,355.32 d. 20,508.99

To solve this, we are going to use the compounded 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 time in years

We know from our problems that she needs $20,857 for a down payment on a house in 9 years, so  and . To convert the interest rate to decimal form, we are going to divide the rate by 100%

Since the interest is compounded quarterly, it is compounded 4 times per year; therefore, . 
Lets replace the values in our formula to find :






We can conclude that the correct answer is: B. 17,633.17