Question

How much do you have to deposit today so that you can withdraw $10,000 a year from years 11 through 13, $15,000 a year from years 14-20, plus an additional amount of $20,000 in year 20. Assume an interest rate of 5% compounded annually.

Answer 1

Find the PV of each of the withdrawals. The sum total would be the amount that needs to be invested today.

A total of $70,286 needs to be invested today to get the desired future payments. Schedule below.

To calculate the Present Value(PV) use either the excel function =PV(rate,nper,pmt,fv), where rate=5, nper=years and FV is the withdrawal amount.

Alternately, we can calculate PV using the formula, PV = FV/(1+rate)^years

Years	Withdrawal (FV)	PV
11	10000	($5,847)
12	10000	($5,568)
13	10000	($5,303)
14	15000	($7,576)
15	15000	($7,215)
16	15000	($6,872)
17	15000	($6,544)
18	15000	($6,233)
19	15000	($5,936)
20	35000	($13,191)
	155000	($70,286)