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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

User Avj
by
8.3k points

1 Answer

2 votes
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.

User Dario Zadro
by
8.2k points
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