Question
In: Accounting
Today is your 22nd birthday. You plan to retire on your 60th birthday, immediately after making...
Today is your 22nd birthday. You plan to retire on your 60th birthday, immediately after making your last savings deposit, and begin collecting your retirement payments on your 61st birthday. You decide that your retirement payment will be $80,000 at age 61, growing at 1.5% per year afterwards, and you expect to collect a total of 35 payments. Starting on your 23rd birthday, and on every birthday before you retire, you will make a deposit into your retirement savings account. Your annual savings deposit will be the same every year.
a)What is your annual deposit if you estimate earning an interest rate of 2% during retirement and an interest rate of 3% before retirement?
b)What is your annual deposit if you estimate the interest rate next year will be 0.5% and will increase by 0.065% each year (i.e. two years from now the interest rate will be 0.565%)?
c)You estimate that you will be able to save $6,000 per year. What rate of return will you need to earn before retirement? (assume the interest rate during retirement is 2%)
d)Analyze the results in parts a, b, and c –which of the three scenarios is most “efficient” in terms of the proportion of your retirement funded by interest earned on your savings? Which of the three scenarios do you think is the most realistic in terms of the amounts saved or the interest rate required?
Solutions
Expert Solution
| Forumala for calculating annual deposits to be made if invested at the end of year | |||||
| P = F X I / [{(1 + I)^N} - 1] | |||||
| where, | |||||
| P - Annual deposits | |||||
| F - Retirement Payment | |||||
| I - Rate of return | |||||
| N - Number of deposits | |||||
| Now | |||||
| As per problem, | |||||
| I - 3% | |||||
| N - 38 | |||||
| Payment expected to be recived at age 61 is $80,000 and post retirement return is 2% | |||||
| Therefore, Fund at age of 60 will be = $80,000 / 102 * 100 = $78,431.37 | |||||
| F - $78,431.37 | |||||
| a) | P | = F X I / [{(1 + I)^N} - 1] | |||
| = $78,431.37 X 0.03 / [{(1 + 0.03)^38} - 1] | |||||
| = $78,431.37 X 0.014459 | |||||
| = $1,134.04 | |||||
| I need to make deposits of $1,134.04 every year | |||||
| b) | If rate of interest will be 0.565% at my 24th birthday then | ||||
| I - 0.565% | |||||
| N - (60-23) = 37 | |||||
| P | = F X I / [{(1 + I)^N} - 1] | ||||
| = $78,431.37 X 0.0565 / [{(1 + 0.00565)^37} - 1] | |||||
| = $78,431.37 X 0.024376 | |||||
| = $1911.87 | |||||
| After trail and error method we get that $1,855.87 should be deposited |
| Age | Opening Balance | Amount Invested | Interest | End Balance | ||
| 23 | $ - | $ 1,855.87 | $ 9.28 | $ 1,865.15 | ||
| 24 | $ 1,865.15 | $ 1,855.87 | $ 10.49 | $ 3,731.51 | ||
| 25 | $ 3,731.51 | $ 1,855.87 | $ 21.08 | $ 5,608.46 | ||
| 26 | $ 5,608.46 | $ 1,855.87 | $ 31.69 | $ 7,496.02 | ||
| 27 | $ 7,496.02 | $ 1,855.87 | $ 42.35 | $ 9,394.24 | ||
| 28 | $ 9,394.24 | $ 1,855.87 | $ 53.08 | $ 11,303.19 | ||
| 29 | $ 11,303.19 | $ 1,855.87 | $ 63.86 | $ 13,222.92 | ||
| 30 | $ 13,222.92 | $ 1,855.87 | $ 74.71 | $ 15,153.50 | ||
| 31 | $ 15,153.50 | $ 1,855.87 | $ 85.62 | $ 17,094.99 | ||
| 32 | $ 17,094.99 | $ 1,855.87 | $ 96.59 | $ 19,047.44 | ||
| 33 | $ 19,047.44 | $ 1,855.87 | $ 107.62 | $ 21,010.93 | ||
| 34 | $ 21,010.93 | $ 1,855.87 | $ 118.71 | $ 22,985.51 | ||
| 35 | $ 22,985.51 | $ 1,855.87 | $ 129.87 | $ 24,971.25 | ||
| 36 | $ 24,971.25 | $ 1,855.87 | $ 141.09 | $ 26,968.21 | ||
| 37 | $ 26,968.21 | $ 1,855.87 | $ 152.37 | $ 28,976.45 | ||
| 38 | $ 28,976.45 | $ 1,855.87 | $ 163.72 | $ 30,996.03 | ||
| 39 | $ 30,996.03 | $ 1,855.87 | $ 175.13 | $ 33,027.03 | ||
| 40 | $ 33,027.03 | $ 1,855.87 | $ 186.60 | $ 35,069.51 | ||
| 41 | $ 35,069.51 | $ 1,855.87 | $ 198.14 | $ 37,123.52 | ||
| 42 | $ 37,123.52 | $ 1,855.87 | $ 209.75 | $ 39,189.14 | ||
| 43 | $ 39,189.14 | $ 1,855.87 | $ 221.42 | $ 41,266.42 | ||
| 44 | $ 41,266.42 | $ 1,855.87 | $ 233.16 | $ 43,355.45 | ||
| 45 | $ 43,355.45 | $ 1,855.87 | $ 244.96 | $ 45,456.28 | ||
| 46 | $ 45,456.28 | $ 1,855.87 | $ 256.83 | $ 47,568.98 | ||
| 47 | $ 47,568.98 | $ 1,855.87 | $ 268.76 | $ 49,693.61 |
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