- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 4. The Future Value and Present Value of a Series of Equal Cash Flows (Ordinary Annuities, Annuity Dues, and Perpetuities)

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**CFA Practice Question**

A 24-year-old is using the following information to plan her retirement:

Expected retirement age: 68

Life expectancy: 93

Current annual expenditures: $30,000

Expected inflation rate of current expenditures until retirement: 3%

Expected return on investment: 8%

Current age: 24

Expected retirement age: 68

Life expectancy: 93

Current annual expenditures: $30,000

Expected inflation rate of current expenditures until retirement: 3%

Expected return on investment: 8%

She assumes her consumption expenditures will increase with the rate of inflation, 3%, until she retires. Upon retiring, she will have end-of-year expenditures equal to her consumption expenditure at age 68. The minimum amount that she must accumulate by age 68 in order to fund her retirement is closest to ______.

A. $928,000

B. $1,176,000

C. $1,552,000

**Explanation:**Her consumption spending (currently $30,000 annually) increases with the rate of inflation (3%) over the next 44 years until she retires. Her annual consumption spending at the time she retires will be $110,143.57 (PV = 30,000, %I = 3, N = 44, solve for FV). To support that level of spending for 25 years of retirement, assuming an 8% return on her retirement account, she must accumulate $1,175,756 by her retirement date (PMT = 110,143.57, N = 25, %I = 8, solve for PV).

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**User Contributed Comments**
4

User |
Comment |
---|---|

linzlinked |
Has expected return included inflation 3%? Shouldn't 3% inflation be added on 8% since it is stated separately here? |

ioanaN |
they assume the cost of living will be constant through out retirement but 110,143 is the inflation adjusted equivalent of the 30,000 in the first year of retirement. and so, the following year the required amount will be 110,143X1.03, and so on. the total cost of living would be sum(110,143X(1.03)^k), k=0to25 |

ioanaN |
and so, why not %I=5?? |

jorgerico3 |
because that interest would affect the total savings not just the cost of living |