Question

Please assist with the following question:

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.2%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.)

Joe $____________

Jill $______________

Answer 1

Joe case   
  
Deposit Annully amount at end (P)=   $5,000
yield rate (i) = 9.2% or   0.092
Time (n) in years =   30

Future value of annuity formula = P *{ (1+r)^n - 1 } / r  
5000 *( ((1+0.092)^30)-1)/0.092  
$707,487.89  

So Amount after 30 years shall be   $707,487.89
  
Jill case  

Annuity amount weekly =   96.15
No of weeks or deposits (30 years *52) =   1560
Annual interest rate will be comoounded weekly.  
So weekly rate = 0.092/52 =   0.001769230769

Future value of annuity formula = P *{ (1+r)^n - 1 } / r  
=96.15*(((1+0.001769230769)^1560)-1)/0.001769230769  
=802215.7037  
  
Value of savings at 30 years =   $802,215.70
  

Excel function = -FV(rate, periods, amount)

For eg in Joe case = -FV(0.092,30,5000)

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