Question

As a forward-thinking individual, you are planning for your retirement. You plan to work for 20 more years. For the next 10 years, you can save $4,000 per year (with the first deposit being made one year from today).In Year 10, you plan to buy a weekend vacation home in the mountains for $40,000. How much must you save annually in years 11 through 20 so that you have exactly $300,000 saved when you retire? Assume you can earn 10%, compounded annually, for each of the next 20 years, and ignore any tax implications associated with your investments.

Answer 1

Future value of Investment at the end of year 10	annual payment*FVAF at 10% for 10 years	4000*15.9374		63749.6
Annual Payment				4000
FVAF at 10% for 10 Years	(1+r)^n-1/ r	(1.1)^10-1 /105	1.59374/10%	15.9374
value in investment account after 10 years
Future value of Investment at the end of year 10			63749.6
purchase cost of vacation house			40000
balance or amount left in investment accounts	63749.6-40000		23749.6
future value of amount left in investment account from year 11-20	balance in investment account*(1+r)^n	23749.6*1.1^10	61600.35
Amount needed at retirement after adjustment to future value of balance in investment account	300000-61600.35		238399.65
Annual payment required to attend 238399.65 in years 11-20	238399.65/15.9374		14958.50
Amount needed at retirement after adjustment to future value of balance in investment account				238399.65
FVAF at 10% for 10 Years	(1+r)^n-1/ r	(1.1)^10-1 /105	1.59374/10%	15.9374
He should save 14958.50 per month to achieve the desired retirement balance of 300000