Question

WILL MARK BRAINILEST!!!!!

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

Answer 1

To solve this we are going to use the compound interest formula with periodic deposits:
`A=P(1+ (r)/(n) )^(nt)+P_(d)( ((1+ (r)/(n))^(nt)-1 )/( (r)/(n) ) )(1+ (r)/(n) )`
where

`A` is the final amount after
`t` years

`P` is the initial investment

`P_(d)` is the periodic deposits

`r` is the interest rate in decimal form

`n` is the number of times the interest is compounded per year

`t` is the time in years

Since he is going to save from 27 years old until 65 years old,
`t=65-27=38`. We know that hes is opening his IRA with $0, so
`P=0`; We also know that he is going to invest $200 at the beginning of each month, so
`P_(d)=200`. To convert the interest rate to decimal form, we are going to divide it by 100:
`r= (2.65)/(100) =0.0265`, and since the interest is compounded monthly,
`n=12`. Lets replace all the values in our formula to find
`A`:

`A=P(1+ (r)/(n) )^(nt)+P_(d)( ((1+ (r)/(n))^(nt)-1 )/( (r)/(n) ) )(1+ (r)/(n) )`

`A=0(1+ (0.0265)/(12) )^((12)(38))+200( ((1+ (0.0265)/(12))^((12)(38))-1 )/( (0.0265)/(12) ) )(1+ (0.0265)/(12) )`

`A=157419.04`

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