Question

show cash flow diagram and all work

wedPuun any. HOW MUCIBUUU JULI pay UGLA W his uncle 9 years later? (30 points) 4 2950 points) You saved $100 at the end of the first year into your savings account. You plan to increase your annual savings by $50 each year for the following 19 years. That is $150 the 2nd year, $200 the 3 year, etc. The bank pays you 10% interest compound annually. What is the maximum amount that you can withdraw from your savings account at the end of the 21st year?

Answer 1

Year 0 1 2 3 4 19 20 21
0 -100 -150 -200 -250 -1000 0 +X

This can be broken down into two series:
Series 1: 19 cash flows of 100 each
Series 2: arithmetic gradient cash flow with n=19 and gradient=50

Present value of constant annuity=A/r*(1-1/(1+r)^n)=100/10%*(1-1/(1+10%)^19)=836.492009173

Present value of arithmetic gradient=

=50/(10%*1.1^19)*((1.1^19-1)/10%-19)=2629.134133

Total present value=836.492009173+2629.134133=3465.626142

Future value at the end of 21st year=present value*(1+r)^21=3465.626142*1.1^21=25646.49966

Hence, Maximum amount withdrawn=25646.49966