Question

Collins wishes to retire in 30 years’ time and has estimated that he will require a
monthly pension income of K24,000 per month for 20 years subsequent to retirement.
Collins will contribute to a retirement fund which will enable her to take out a monthly
pension of K24,000 after retirement. The retirement fund is currently earning a return of
9% per annum, interest compounded monthly, and this level is expected to remain
unchanged and to be sustainable over the next 50 years. Determine the monthly
contribution that collins is required to make to the retirement fund over the next 30 years.

Answer 1

Annuity starting monthly after retirement (P) =   24,000.00  
Time in months = (n) = 20*12=   240  
interest rate per month (i) = 9℅/12=   0.0075  
      
Present Value of annuity formula =( P *(1-(1/(1+i)^n))/i)      
=24000*(1-(1/(1+0.0075)^240))/0.0075)      
=2,667,478.90      
      
So before retirement K2,667,478.90 would be required to provide K24000 pension after retirement, it means after 30 years.       

Amount is now Future value for today= 2,667,478.90  
Time in months (n)=30*12=   360  
interest rate per month (i) = 9℅/12=   0.0075  
Future value of annuity formula = P *{ (1+i)^n - 1 } / i      
2,667,478.90   = P*(((1+0.0075)^360)-1)/0.0075  
2,667,478.90   =P*   1830.743483
P= 1,457.05  

So amount required to contribute each month is K1,457.05