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One day, your aunt Mary calls you and seeks your advice on some financial matters
One day, your aunt Mary calls you and seeks your advice on some financial matters. Mary is a designer with two children. She is planning for retirement in 20 years. Currently, she has $200,000 in a savings account and $400,000 in a mutual fund. Moreover, she plans to add to her savings by depositing $5,000 per month in her savings account at the end of each month until retirement. The investment in the savings account will return 12% APR compounded monthly and the investment in the mutual fund will return 10% APR compounded annually. Mary expects to live for 30 years after she retires and at retirement she will deposit all of her investments in a bank account paying 6% APR compounded monthly. In addition, she would like to have a total of $3,000,000 to leave to her children when she passes away. Required: a. How much will Mary have when she retires? (20 marks) b. How much can Mary withdraw each month after retirement? (10 marks) c. Without doing any calculation, critically discuss how an increase in retirement age may affect the amount that Mary can withdraw each month after retirement.
Expert Solution
ANSWER -
| FUTURE VALUE IN SAVINGS ACCOUNT | |||||||||||||
| Rate | Monthly Return =(12/12)% | 1% | |||||||||||
| Nper | Number of months savings | 240 | (20*12) | ||||||||||
| Pmt | Monthly savings | $5,000 | |||||||||||
| Pv | Current Savings | $200,000 | |||||||||||
| FV | Future Value in Savings Account | $7,124,788 | (Using FV function of excel with Rate =1%, Nper=240, Pmt=-5000,Pv=-200000) | ||||||||||
| FUTURE VALUE IN MUTUAL FUND ACCOUNT | |||||||||||||
| Rate | Annual Return | 10% | |||||||||||
| Nper | Number of Years | 20 | |||||||||||
| Pv | Current Savings | $400,000 | |||||||||||
| FV | Future Value in Mutual Fund Account | $2,691,000 | (Using FV function of excel with Rate =10%, Nper=20, Pv=-400000) | ||||||||||
| (a) | |||||||||||||
| A | Amount in Savings Account | $7,124,788 | |||||||||||
| B | Amount in Mutual Fund Account | $2,691,000 | |||||||||||
| C=A+B | Amount Mary will have when she retires | $9,815,788 | |||||||||||
| (b) | |||||||||||||
| Rate | Monthly Interest rate after retirement=(6/12)% | 0.50% | |||||||||||
| Nper | Number of months of withdrawal | 360 | (30*12) | ||||||||||
| Pv | Amount available at the time of retirement | $9,815,788 | |||||||||||
| Fv | Amount left for children | $3,000,000 | |||||||||||
| PMT | Amount of monthly withdrawal | $55,864.09 | (Using PMT function of excel with Rate =0.5%, Nper=360, Pv=-9815788,Fv=3000000) | ||||||||||
| c) | Increase in retirement age will, | ||||||||||||
| Increase the amount available at retirement | |||||||||||||
| will reduce the number of months of withdrawal | |||||||||||||
| Consequently will increase monthly withdrawal |
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