Question

8) Your client is 25 years old and wants to start receiving payments of $100,000 per year when she retires on her 60th birthday until her 89th birthday. As her financial advisor, how much must she invest every year staring today to achieve her goal if she can earn 7 percent annual interest?

9)

Calculate the expected rate of return for an investment of $550,000. What does the expected rate of return mean?

Dollar amount of Return |
Probability of Outcome |

$100,000 |
.05 |

50,000 |
.50 |

10,000 |
.30 |

- 20,000 |
.15 |

Answer #1

8. Present value of annuity = P* [ [1- (1+r)^{-n} ]/r
]

P = Annual payment = $100,000.00

r = Rate of interest = 7%

n = Number of years = 30

Present value of annuity = 100000* [ (1- (1+0.07)^-30)/0.07 ] = $1,240,904.12

Payment required = FV*r /[(1+r)^n -1] * 1/(1+r)

= 1240904.12*0.07/ [(1+0.07)^35 -1] *1/(1+0.07) = $8,389.39

9. Expected return = Expected dollar return/ Amount of
investment * 100

= 36,000/ 550,000 *100= 6.55%

It means that it is expected to earn 6.55% on its investment after taking into consideration all possible probable outcomes.

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