Question

Mario and his dad decide to start saving for retirement at the same time. Mario is 20 years old and his dad is 40 years old. Both plan to put money into an IRA until they are 65. Both invest in the same things and earn the same rate of​ return, which is 7​%. ​ Finally, in their retirement​ years, both believe they can score an APR of 4​%. If they both want to receive ​$4000 per month during​ retirement, then how much does each have to save now if they each plan to live an additional 25 years in​ retirement? The dad would need to save ​$nothing per​ month, rounded to nearest cent. Mario would need to save ​$nothing per​ month, rounded to nearest cent.

Answer 1

Mario:

we must first calculate the present value of Mario's distributions when he retires:

present value = monthly distribution x annuity factor

• monthly distribution = 4,000
• PV annuity factor, 300 periods, 0.333% = 189.53178

present value = 4,000 x 189.53178 = $758,127.12

he will make 45 years of contributions to his IRA, which totals 540 monthly contributions

we are not told if the interest rate is effective or not, and how often is interest compounded, so I will just divide it by 12 to calculate the monthly interest rate (same as before) = 0.583333%

the future value of Mario's contributions = monthly contribution x annuity factor

future value = $758,127.12

FV annuity factor, 540 periods, 0.583333% = 3,792.58975

monthly contribution = $758,127.12 / 3,792.58975 = $199.90

Mario's dad:

present value of the annuity when he is 65 = $758,127.12 (same as Mario's)

the future value of his contributions = monthly contribution x annuity factor

future value = $758,127.12

FV annuity factor, 300 periods, 0.583333% = 810.07118

monthly contribution = $758,127.12 / 810.07118 = $935.88