Susan would like to receive $70,000 in the first year of her financial independence at age 60. After this first income payment, she is content with her annual income growing at the rate of 2% per annum below the rate of inflation. She would like this income to be paid indefinitely. She expects inflation to be 3% per year and her investments to achieve nominal returns of 6% per year (compounded yearly). Assuming that all calculations are to be performed in ‘real’ terms, how much does she need to save for financial independence (to the nearest dollar)
Question
Susan would like to receive $70,000 in the first year of her financial independence at age 60. After this first income payment, she is content with her annual income growing at the rate of 2% per annum below the rate of inflation. She would like this income to be paid indefinitely. She expects inflation to be 3% per year and her investments to achieve nominal returns of 6% per year (compounded yearly). Assuming that all calculations are to be performed in ‘real’ terms, how much does she need to save for financial independence (to the nearest dollar)
Solution
To solve this problem, we need to use the formula for the present value of a growing perpetuity. The formula is:
PV = D / (r - g)
where:
- PV is the present value, or how much Susan needs to save.
- D is the dividend, or the annual income Susan wants to receive. In this case, it's $70,000.
- r is the discount rate, or the rate of return on Susan's investments. Since we're working in real terms, we need to adjust the nominal return for inflation. The real rate of return is approximately the nominal rate minus the inflation rate, so r = 6% - 3% = 3%.
- g is the growth rate of the dividend. Susan wants her income to grow 2% below the rate of inflation, so g = 3% - 2% = 1%.
Substituting these values into the formula, we get:
PV = 70,000 / 2% = $3,500,000
So, Susan needs to save approximately $3,500,000 for financial independence.
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