Ms. Ieda Silva plans to retire in 30 years and expects to live for 20 years afte
ID: 2717794 • Letter: M
Question
Ms. Ieda Silva plans to retire in 30 years and expects to live for 20 years after retirement. She is preparing a savings plan to meet the following objectives. First, after retirement she would like to be able to withdraw $20,000 per month. The first withdrawal will occur at the end of the first month after retirement. Second, she would like to leave her son an inheritance of $500,000 when she passes on. Finally, she would like to set up a fund that will pay $5,000 per month forever to her favorite charity after she passes on. These payments to the charity will start one month after she passes on. All monies can earn 10 percent annual rate compounded monthly. How much will she have to save per month to meet these objectives? She wishes to make the first deposit a month from now and the last deposit on the day she retires.
Please show work!
Explanation / Answer
Compound interest formula:
A = P (1+r/n) ^ nt
Rate of interest is 10% which is 0.1 (decimal) which is r. so r = 0.10
No. of years is 30. Since she makes first deposit now and last deposit is on the day she retires. She is planning to retire in 30 years. Therefore, No. of years which is t = 30
All monies can earn 10 percent annual rate compounded monthly. Therefore n=12
Let’s say for charity purpose she will set up a fund that will pay $5,000 per month forever. For this she has to pay a premium of $5,000 every month for 30 years. Therefore, the amount will be $1,800,000.
After retirement she would like to be able to withdraw $20,000 per month and expects to live for 20 years after retirement, so that amount will be 4,800,000. Therefore, A = 1,800,000 + 4,800,000 which gives as A = 6,600,000
Therefore to find the principal amount which is saved by her per month is calculated as follows:
6600000 = P (1+0.1/12) ^ (30*12)
6600000 = P (1+0.00833) ^ (360)
6600000 = P (1.00833) ^ (360)
6600000 = P (19.81380)
6600000/19.81380 = P
333101 = P
Therefore, she has to save $3,33,101 every month to execute her plans
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