Question

Ian Krassner wants to save money to meet two objectives. First, he wants to retire 30 years from today with a retirement income of $300,000 per year for 20 years. The first retirement payment will occur 31 years from today. Second, he would like to purchase a cabin in the mountains 10 years from today at an estimated cost of $350,000. He can afford to save only $40,000 at the end of each year for the first 10 years. He expects to earn 7 percent per year on his savings. Assuming he saves the same amount each year, what must Ian save annually at the end of year 11 through year 30 to meet his objectives?

Answer 1

Retirement income for 20 years =300000 per year
Rate =7%
Value of Retirement fund 30 years from today =PMT*((1-(1+r)^-n)/r) =300000*((1-(1+7%)^-20)/7%) =3178204.2737

Savings each year for 10 years =400000
Value of savings at the end of 10 years =PMT*((1+r)^n-1)/r) =40000*((1+7%)^10-1)/7%) =552657.9185
Amount to purchase cabin at year 10 =350000
Amount remaining in account after 10 years =552657.9185-350000 =202657.9185

Amount in account after 10 Years*(1+r)^20+Savings form year 11-30*((1+r)^n-1)/r) =Value of Retirement fund 30 years from today
202657.9185*(1+7%)^20+PMT*(((1+7%)^20-1)/7%) =3178204.2737
PMT*40.99549 =3178204.2737-202657.9185*(1+7%)^20
PMT =(3178204.2737-202657.9185*(1+7%)^20)/40.99549=58396.23