Will mark ! ralph is 27 years old and starting an ira (individual retirement account). he is going to invest $200 at the beginning of each month. the account is expected to earn 2.65% interest, compounded monthly. how much money will ricky have in his ira when he retires, at age 65? $157,419.08 $94,723.10 $13,183.51 $416,424.15

To solve this we are going to use the compound interest formula with periodic deposits: 
where 
is the final amount after  years 
is the initial investment 
is the periodic deposits
is the interest rate in decimal form 
is the number of times the interest is compounded per year 
is the time in years

Since he is going to save from 27 years old  until 65 years old, . We know that hes is opening his IRA with $0, so ; We also know that he is going to invest $200 at the beginning of each month, so . To convert the interest rate to decimal form, we are going to divide it by 100: , and since the interest is compounded monthly, . Lets replace all the values in our formula to find :




We can conclude that Rick will have $157,419.04 in his IRA account by the time when he retires.