Question
In: Finance
Your 40-year clients, who have a 12-year old child, plan to retire at the age of...
Your 40-year clients, who have a 12-year old child, plan to retire at the age of 62. Assume 360-day year and 30-day month in your calculations.
They have a current salary at an annual rate of $144000, being paid equally at the end of each month. They expect a 3% raise in their salary every year until they retire. They deposit 12% of their monthly salary to their 401(k) account that generates an annual rate of return of 10%, compounded daily. In addition, their employer matches their contribution with 5% of their salary to the same 401(k) account.
At the end of each year, your clients will receive a bonus of 15% of their annual salary. Your clients commit to deposit part of their annual bonus, $15,000, in a 529 Plan account each year for financing their child’s college education. They will keep contributing to the 529 account until their child finishes college. Any remaining amount from the annual bonus check will be deposited in an IRA account. Both of these accounts are expected to generate an annual rate of return of 9%, compounded monthly.
1. Determine the cash flows pattern of their contributions to the IRA account; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. And calculate their IRA account balance upon their retirement.
2. Determine the cash flows pattern of their contributions to the 529 Plan account; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. And calculate the 529 Plan account balance at the time their child starts college.
Solutions
Expert Solution
| Assumptions | 360 day year and 30 days a month | Return | 9% | compounded monthly | |||||||||||||||||||
| Current Salary | $ 144,000 | Rate of Return | 0.8% | ||||||||||||||||||||
| Rise | 3% | ||||||||||||||||||||||
| 12% deposited to 401K account | |||||||||||||||||||||||
| End of each year | 15% | bonus of annual salary | |||||||||||||||||||||
| $ 15,000 | deposited in 529 plan account | ||||||||||||||||||||||
| Remaining amount deposited in an IRA account | |||||||||||||||||||||||
| $ 6,600 | |||||||||||||||||||||||
| IRA and 529 Cash Schedule | |||||||||||||||||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
| Salary | $ 144,000 | $ 148,320 | $ 152,770 | $ 157,353 | $ 162,073 | $ 166,935 | $ 171,944 | $ 177,102 | $ 182,415 | $ 187,887 | $ 193,524 | $ 199,330 | $ 205,310 | $ 211,469 | $ 217,813 | $ 224,347 | $ 231,078 | $ 238,010 | $ 245,150 | $ 252,505 | $ 260,080 | $ 267,882 | $ 275,919 |
| Bonus | $ 21,600 | $ 22,248 | $ 22,915 | $ 23,603 | $ 24,311 | $ 25,040 | $ 25,792 | $ 26,565 | $ 27,362 | $ 28,183 | $ 29,029 | $ 29,899 | $ 30,796 | $ 31,720 | $ 32,672 | $ 33,652 | $ 34,662 | $ 35,702 | $ 36,773 | $ 37,876 | $ 39,012 | $ 40,182 | $ 41,388 |
| 529 Plan | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 | $ 15,000 |
| IRA account | $ 6,600 | $ 7,248 | $ 7,915 | $ 8,603 | $ 9,311 | $ 10,040 | $ 10,792 | $ 11,565 | $ 12,362 | $ 13,183 | $ 14,029 | $ 14,899 | $ 15,796 | $ 16,720 | $ 17,672 | $ 18,652 | $ 19,662 | $ 20,702 | $ 21,773 | $ 22,876 | $ 24,012 | $ 25,182 | $ 26,388 |
| Compounded Annual Return for IRA Account | $ 47,450 | $ 47,640 | $ 47,565 | $ 47,263 | $ 46,766 | $ 46,104 | $ 45,304 | $ 44,388 | $ 43,378 | $ 42,291 | $ 41,144 | $ 39,950 | $ 38,723 | $ 37,472 | $ 36,208 | $ 34,939 | $ 33,672 | $ 32,412 | $ 31,165 | $ 29,936 | $ 28,728 | $ 27,545 | $ 26,388 |
| Compounded Annual Return for 529 Account | $ 107,841 | $ 98,593 | $ 90,137 | $ 82,407 | $ 75,340 | $ 68,878 | $ 62,971 | $ 57,571 | $ 52,633 | $ 48,119 | $ 43,993 | $ 40,220 | $ 36,770 | $ 33,617 | $ 30,734 | $ 28,098 | $ 25,688 | $ 23,485 | $ 21,471 | $ 19,630 | $ 17,946 | $ 16,407 | $ 15,000 |
| I used compounded monthly because in question it is given that the rate of return is 9% compounded monthly | |||||||||||||||||||||||
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