John is considering investing in an annuity. He expects to invest anywhere between 5% and 20% of his monthly income. John currently makes $72,000 per year and expects an average raise of 4% in his salary until he retires; he doesn't know exactly when he will retire but expects that it will be anywhere from 15 to 20 years from today. The annuity's interest rates (depending on the time period) are listed below:
|
Time Length of Annuity
|
Expected Effective Annual Interest Rate (%)
|
|
15
|
4.25
|
|
16
|
4.00
|
|
17
|
3.95
|
|
18
|
3.75
|
|
19
|
3.60
|
|
20
|
3.50
|
Find the optimal annuity value for John, that is, for how many years John should work and how much he should invest every month.