Question

Use the savings plan formula to answer the following question. A friend has an IRA with an APR of 5.75​% She started the IRA at age 19 and deposits ​$100 per month. How much will her IRA contain when she retires at age​ 65? Compare that amount to the total deposits made over the time period. After retirement the IRA will contain ​$ ____________

How many total deposits were made? ____

Answer 1

After retirement the IRA will contain ?$
Future Value of an Ordinary Annuity
= C*[(1+i)^n-1]/i
Where,
C= Cash Flow per period
i = interest rate per period =5.75/12 =0.47916667%
n=number of period =(65-19)*12 =552
= $100[ (1+0.00479166667)^552 -1] /0.00479166667
= $100[ (1.00479166667)^552 -1] /0.00479166667
= $100[ (13.9948 -1] /0.00479166667]
= $271,195.06
Total deposits = (65-19)*12
=552