Question

7. Suppose you buy your home when you are 35. and so it will be paid off by the time you are 65, when you retire. It would be wise to save enough money to take monthly payouts until you are age 90 Older people who no longer have an income often move their investments to a more secure, lower-interest option because these investments are less likely to crash or suddenly lose all their value. Suppose you move your annuity from the 4% rate you had been earning while you were ages 35- 65 to a safer annuity earning 2.96% (the highest guaranteed long-term annuity rate) during the ages from 65-90. It is from this safer annuity that you will take monthly payouts. How much will you have to put into your monthly annuity earning 4% from the age of 35 to the age of 65 if you wish to receive monthly payouts of a. $3000? b. $5000? c. $8000? 8. Challenge: How long will it take to earn $1,000,000 by depositing $740 every two weeks into an annuity that earns 6% annual interest? 9 tax brakets

8

Answer 1

7-a). Monthly payout of $3,000:

Funds needed at retirement: PMT = 3,000; N = (90 - 65)*12 = 300; rate = 2.96%/12 = 0.247%, solve for PV.

Funds needed = 635,413.57

So, from age 35 to 65, amount collected has to save up to 634,413.57 at an annual rate of 4%.

PV = 0; FV = -635,413.57; N = 30*12 = 360; rate = 4%/12 = 0.33%, solve for PMT.

Monthly annuity = $915.52

7-b). Monthly payout of $5,000:

Funds needed at retirement: PMT = 5,000; N = (90 - 65)*12 = 300; rate = 2.96%/12 = 0.247%, solve for PV.

Funds needed = 1,059,022.61

PV = 0; FV = -1,059,022.61; N = 30*12 = 360; rate = 4%/12 = 0.33%, solve for PMT.

Monthly annuity = $1,525.86

7-c). Monthly payout of $8,000:

Funds needed at retirement: PMT = 8,000; N = (90 - 65)*12 = 300; rate = 2.96%/12 = 0.247%, solve for PV.

Funds needed = 1,694,436.18

PV = 0; FV = -1,694,436.18; N = 30*12 = 360; rate = 4%/12 = 0.33%, solve for PMT.

Monthly annuity = $2,441.38

8). Number of payments made in a year = 52/2 = 26 (since deposit is made every 2 weeks)

Interest rate = 6%/26 = 0.231%

PV = 0; PMT = 740; FV = -1,000,000; rate = 0.231%, solve for Nper.

Number of deposits to be made = 614.09

Number of years = 614.09/26 = 23.62 years.