Question

Fred and Wilma want to save money to provide for their retirement and for the education of their daughter Pebbles. Pebbles will need $25,000 annually for four years beginning 15 years from now. Fred and Wilma figure that they will both retire 30 years from now and would like to have $100,000 annually for 25 years (with the first withdrawal beginning one year after their retirement). Given an interest rate of 9%, how much must Fred and Wilma invest annually if they plan to begin making deposits in one year and will make 30 deposits in all?

I have the solution ($9,565) but am struggling with the steps

Answer 1

Don't Worry Try with me Step by Step.

Step 1: Calculate the Balance needed after 30 years so that she can get annual withdrawal of 100000 for 25 years, Rate 9% that means you need to calculate the present value of these payments.

PV = Annual cash flows x cumulative discounting factor @9% for 25 years

Pv = 100000 x 9.82258

PV = 982258 approx

Step 2 Calculate the Future value of the fees required after 15 years rate 9% so that it will become at same time as step 1 i.e. at time 30.

= 25000(1.09)¹⁵ + 25000(1.09)¹⁴ + 25000(1.09)^{13 +} 25000(1.09)¹²

⁼ 91062.06 + 83543.18 + 76645.12 + 70316.62

= 321567 approx

Step 3 Add the Value Step1 and step 2. This amount you need to accumulate with 30 deposits at 9%

Accumulated Amount = 982258 + 321567 =1303825

Step 4: Calculate the Annual Saving Required

you need Excel or financial calculator

Put values in texas ba 2 as N=30,I/Y=9,PV=0, FV = 1303825 Compute PMT = 9565

You can calculate the above alternatively if you have cumulative annuity table as

1303825 = Annual Payment x cumulative annuity factor @ 9% for 30 years.