Barry Cuda currently has $35,000 in his Roth IRA which has been earning 7%. Barry is planning on depositing $5500 annually for the next 40 years into this IRA. Assuming Barry's IRA continues earning 7% annually, what will Barry's IRA be worth at the end of 40 years?

Total worth of worth of investment= $1,622,099.14  

Explanation:

The total amount available in his account would be determined as follows:

The value of the existing current amount in 40 years time

FV =  PV × (1+r)^ n

FV- future value

PV- current amount in account

r- interest rate

n- number of years

FV =  35,000 × (1.07)^(40=

FV=  524,106.02  

The value of the new annual deposit of 5,500 in 40 years time

This represents an annuity. An annuity is series of constant but equal amount  occurring for a certain number of years .

FV= A×( (1+r) -1)/r

FV - future value

R - interests rate

n- number of years

A- annual deposit

FV = 5,500 × ((1+0.07)^40 -1)/0.07

FV=  1,097,993.12  

Total worth of worth of investment

=   524,106.02   + 1,097,993.12  = 1,622,099.14  

Total worth of worth of investment= $1,622,099.14