You can deposit $4000 per year into an account that pays 12% interest. If you deposit such amounts for 15 years and start drawing money out of the account in equal annual installments, how much could you draw out each year for 20 years?

The question involves annuities and requires two steps, the calculation of the future value after 15 years of deposits into an account with a 12% interest rate and then the calculation of the equal annual withdrawals for 20 years from that future value. The result is $10,686.54.

Explanation:

This is a question about annuities, which are a series of equal payments made at regular intervals. In this case, the annuity involves both the depositing of funds into the account and also the withdrawal of the funds. So it is a combination of an ordinary annuity (the deposit phase) and an annuity due (the withdrawal phase).

For the deposit phase, using the formula for the future value of an ordinary annuity which is PMT × [(1 + r)^n - 1] / r, where PMT is the annual payment ($4000), r is the annual interest rate (12% or 0.12), and n is the number of years (15). The future value after 15 years would be $138,003.48.

For the withdrawal phase, we have to calculate the amount that can be withdrawn each year given the future value which is an annuity due problem. The formula for this is PV = PMT × [1 - (1 + r)^-n] / r, where PV is the present value, which in this case is the future value from the first phase ($138,003.48). Solving for PMT, we get $10,686.54.

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