Final answer:
To calculate the present value of the cash flows, use the present value of an ordinary annuity formula for the annual withdrawals, and the present value of a lump sum formula for the final sum. Total them and discount back to today to find the required today's deposit.
Step-by-step explanation:
To calculate the present value of complex cash flows starting 11 years from now with withdrawals of $58,000 a year for 4 years and an additional $16,000 in the last year at an interest rate of 6%, we need to discount each of those future cash flows back to their present value.
Firstly, we calculate the present value of the ordinary annuity, which is the series of equal payments of $58,000, using the formula:
Present Value (PV) = PMT [1 - (1 + r)^-n] / r,
Where PMT is the annual payment, r is the annual interest rate, and n is the number of payments.
Then, we calculate the present value of the single additional payment of $16,000 occurring at year 14, using the present value of a lump sum formula:
PV = FV / (1 + r)^n,
Where FV is the future value of the lump sum.
After finding the present values, we sum them up and discount them back to 'today,' which is 11 years before the first withdrawal, to find the total amount that needs to be deposited today. Using financial calculators or present value tables can simplify this process.