Question

75. Calculating Growing Annuities (LO1) You have 40 years left until retirement and want to retire with $5 million. Your salary is paid annually, and you will receive $50,000 at the end of the current year. Your salary will increase at 3 percent per year, and can earn a 10 percent return on the money you invest. If you save a constant percentage Show this Ior vout pr CoU you of your salary,what percentage of your salary must you save each year? C-1

Answer 1

The return to be earned on retirement savings depend on allocation by individual.

In the last 30 years, the historical returns on stock has been 10% per year, while average bond return has been 5%. These are nominal returns

let annual savings be denoted by x

Given,

increment rate = 3%

Using the present value formula,

5000000= x*(1.1^40 -1.03^40)/ (0.1-0.03)

x = 5000000*0.07/ (1.1^40 -1.03^40) = 8333.88

The proportion of salary to be saved = 8333.88/50000 = 16.67%

Hence. 16..67% of salary must be saved

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