Question

A person will retire 25 years from today and wants to have the retirement annuities $4000 at the end of every month for 20 years since his date of retirement. For this purpose he plans to invest amount 2X at the end of every month for the next 15 years, starting immediately and amount X at the end of every month for the following 10 years (i.e. after the end of 15 years tenure). If the nominal rate of interest 9% per annum convertible monthly for the first 25 years and 6% per annum convertible monthly for the next 20 years, find the value of X.

Answer 1

2X/(9%/12)*((1+9%/12)^(12*15)-1)*(1+9%/12)^(12*10)*(1+9%/12)+X/(9%/12)*((1+9%/12)^(12*10)-1)*(1+9%/12)=4000/(6%/12)*(1-1/(1+6%/12)^(12*20))

=>X=(4000/(6%/12)*(1-1/(1+6%/12)^(12*20)))/(2/(9%/12)*((1+9%/12)^(12*15)-1)*(1+9%/12)^(12*10)*(1+9%/12)+1/(9%/12)*((1+9%/12)^(12*10)-1)*(1+9%/12))

=>X=270.49