Question

A man is planning to retire in 25 years. He wishes to deposit a regular amount every three months until he retires, so that, beginning one year following his retirement, he will receive annual payments of $80,000 for the next 15 years. How much must he deposit if the interest rate is 6% compounded quarterly?

Answer 1

6% compounded quarterly

(1+6%/4)^4-1=6.1364%

FW after 25 years from now of $80000 for 15 years after 25 years=80000(1-(1/1.061364)^15)/(1-(1/1.061364)=$817358.4

x(1.061364)^24.75+x(1.061364)^24.50+x(1.061364)^24.25+(1.061364)^24+x(1.061364)^23.75+x(1.061364)^23.5+x(1.061364)^23.25+x(1.061364)^23+x(1.061364)^22.75+x(1.061364)^22.5+x(1.061364)^22.25+x(1.061364)^22+x(1.061364)^21.75+x(1.061364)^21.5+x(1.061364)^21.25+x(1.061364)^21+x(1.061364)^20.75+x(1.061364)^20.5+x1.061364)^20.25+x(1.061364)^20+x(1.061364)^19.75+x(1.061364)^19.5+x(1.061364)^19.25+x(1.061364)^19+x(1.061364)^18.75+x(1.061364)^18.5+x(1.061364)^18.25+x(1.061364)^18+x(1.061364)^17.75+x(1.061364)^17.5+x(1.061364)^17.25+x(1.061364)^17+x(1.061364)^16.75+x(1.061364)^16.5+x(1.061364)^16.25+x(1.061364)^16+x(1.061364)^15.75+x1.061364)^15.5+x(1.061364)^15.25+x(1.061364)^15+x(1.061364)^14.75+x(1.061364)^14.5+x(1.061364)^14.25+x(1.061364)^14+x(1.061364)^13.75+x(1.061364)^13.5+x(1.061364)^13.25+x(1.061364)^13+x(1.061364)^12.75+x(1.061364)^12.5+x(1.061364)^12.25+x(1.061364)^12+x(1.061364)^11.75+x(1.061364)^11.5+x(1.061364)^11.25+x1.061364)^11+x(1.061364)^10.75+x(1.061364)^10.5+x(1.061364)^10.25+x(1.061364)^9.75+x(1.061364)^9.5+x(1.061364)^9.25+x(1.061364)^9+x(1.061364)^8.75+x(1.061364)^8.5+x(1.061364)^8.25+x(1.061364)^8+x(1.061364)^7.75+x(1.061364)^7.5+x(1.061364)^7.25+x(1.061364)^7+x(1.061364)^6.75+x(1.061364)^6.5+x(1.061364)^6.25+x(1.061364)^6+x(1.061364)^5.75+x(1.061364)^5.5+x(1.061364)^5.25+x(1.061364)^5+x(1.061364)^4.75+x(1.061364)^4.5+x(1.061364)^4.25+x(1.061364)^4+x(1.061364)^3.75+x(1.061364)^3.25+x(1.061364)^3+x(1.061364)^2.75+x(1.061364)^2.5+x(1.061364)^2.25+x(1.061364)^2+x(1.061364)^1.75+x(1.061364)^1.5+x(1.061364)^1.25+x(1.061364)^1+x(1.061364)^0.75+x(1.061364)^0.5+x(1.061364)^0.25

After sloving using solver n excel we get X= 4054,765

Hence he must deposit $4054.77