Question

You wish to have $200,000 at the end of twenty years. In the last five years, you withdraw $1,000 annually at a rate of 3.8% compounded quarterly. During the middle ten years, you contribute $500 monthly at a rate of 2.8% compounded semi-annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly.

The answer is $9,056.65. However, I don't know how they got that answer ...

Answer 1

The below solution is with financial calulator(I used BAII PLUS-TEXAS INSTRUMENT)

This should be the approach:

First of all we have to come from end to start:

therefore FV=200,000

We have to find out PV at end of 15th year:

PMT=1000

P/y=1

C/y=4

PV=-170010.2993

Now this will become FV for investments starting from year 6th to 15th:

FV=170010.2993

PV=?

I/y=2.8

P/y=12

C/y=2

PMT=-500

PV= -52319.866

then this PV will become my FV for investments to be done form year1 to year 5:

SO PV=0

FV=52319.866

i/y=4

p/y=1

c/y=12

PMT = 9645.30

As I am not getting the exact answer, but the approach is right.(there could be problem error in end or begining of cash flows)