Question(HELP): What if he just received a gift of $30,000 from his grandfather and investment that in the same investment account? How much does he need to save each month?

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Given a rate of return of 4.25% for the foreseeable future, how much does he need to save each month until the month before he retires?

Step 1 : Let X be the amount he needed as first retirement income = 5000*(1 + 1.5%/12)⁴⁶⁸ = 8972

Total amount at the retirement he required just after his retirement is monthly annuity he will receive from the insurance company and lumpsum amount of 50000 = 8972+50000 = $58972

Step 2 : Assuming that , he will live for 30 years (360 months) after retirement and getting the monthly payment = 8972 + 8972+ 8972+..........

But we will calculate these values assuming discount rate as 4.25% annual = 8972*(P/A,4.5%/12,360)

= 8972*((1.003542)³⁶⁰ -1)/((1.003542)³⁶⁰ *0.003542) = 1823800

Total amount required in all the retirement years/months , value of all those payments 1 month prior to retirement = 1823800

Step 3 : Let's add the 2% premium cost as well in this amount = 1.02*1823800 = 1860276

And if we add vacation cost also = 1860276 +50000*1.02 = 1911276

Step 4: Now this value needs to be spread over the 467 months which will get us monthly savings.

Monthly saving = 1911276*(A/F, 4.25%/12, 467) = 1911276* ((0.003542)/(1.003542)⁴⁶⁷ -1 ) = 1911276*0.000841 = 1607(approx.)

Monthly saving each month required = 1607

Your 21-year-old client just graduated from college and started a job with monthly salary of $5,000 per month. He wants to retire when he is 60 years old and wants to start saving for retirement right away. We cannot be sure of how long we live after retirement, but the client wants to be extra careful and save for 30 years of after retirement life. Market expectation for average annual inflation for the future is 1.5% (Lets assume inflation to be 0 after retirement period). Because of inflation, he will need substantially higher retirement monthly income to maintain the same purchasing power. He plans to purchase a lifetime annuity from an insurance company one month before he retires, where the retirement annuity will begin in exactly 39 years (468 months). The insurance company will add a 2.00 percent premium to the pure premium cost of the purchase price of the annuity. The pure premium is the actuarial cost of his anticipated lifetime annuity. He also wants to take a big vacation as soon as he retires. He is anticipating that he will need $50,000 for that (at the end of 467 months of saving). He has just learned the concept of time value of money and never saved anything earlier. He will make the first payment in a month from now and the last payment one month before he retires (a total of 467 monthly payments).