Question

You are planning for your pension plan that you will start to invest money, deposit first saving a year from today, deposit last at 20, and get retired after 20 years. You desire to take an immediate trip, costing approximately 15000 TL.(t=20) when you retire, and expect to live 25 more years, for which you need 12000TL each year, starting from one year from retirement. Your savings will be equal and on annual basis. Savings will earn 10% annually. a) How much you should save each year to accomplish your goals? b) What would be the equal savings if pension plan requires semiannual deposits? You still earn 10% annually

3 You are planning for your pension plan that you will start to invest money, deposit first saing a year fom today, deposit last at 20, and get retired after 20 years. You desine to rake an inumediate irip, costing approsimalely 15000 TL.(0-20) when you retire, and expect t lie 25 more vears, for which you need 12000)TL each year, starting from one year from retirement. Your har ings will be equal and on annual basis. Savings will earn 10% annually. a How much you should save each year to accomplish your goals? b What would be the equal savings if pension plan requires semiannual deposits? You sill u 10% annually

Answer 1

Answer (a) For 1 to 20 years a fixed amount has to deposit and at 20th year 15000 withdrawn for tour and from 21 to 45th year i.e., 25 years from 20th year want to withdraw 12000 per year So present value of cash inflows should equal to present value of cash outflow 2 Discounting factor Discounted Cash flows Year 1-20 20 21-45 Particulars Amount (10% Cash outflow -X Cash inflow Cash inflow 8.5184-8.5184x 15000 0.149 2235 12000 1.3619 16342.8 -8.5184x+2235+16342.8 E-8.5184x+18577.8 x= 18578/8.5184 2180.903 Therefore need to deposit an amount of 2181 each year to get 12000 each year from 21st year to 45th year and 15000 at the end of 20th year Note: Discounting factor cummulative of 10% each year

Answer (b) For each two semi annual periods comes to one full year and 10% interest rate divided to half-yearly comes to 5% each period 2 Discounting factor(5% each Discounted Cash flows Periods 1-40 periods(20years) Cash outflow |-x 40th period 21 vear to 45 year Particulars Amount lperiod 17.1827-17.1827x Cash inflow Cash inflow 15000 0.1429 2143.5 12000 1.3619 16342.8 --17.1827x+2413+16343 x= X- 18487/17.1827 1075.867 If needed semi-annual deposit then the deposit amount will be 1076 each half yearly which comes to 2152 each year. When compared to full ear 2181 the half vear depsoit is 2152 only saving 29 each vear. This effect is due to compounding half-yearl Note: Discounting factor for 21-45 year taken at 10% because the receipts are annually but deposits made initially are half-yearly for which 5% rate taken for first 20 years (or) 40 periods.