Question

Lucy retires in 25 years from now and she has two objectives to attain. The first objective is to receive $45,000 per year for forty years once she retires in 25 years. The second objective is to buy jewelry with the estimated cost of $50,000 in 10 years from now. She pays $6000 per month at the rate of 5% interest to save the amount for her objectives for 10 years from now. Find out the annual payment between the years 11 years to 25 years?

Answer 1

Annuity required after retirement (P) =   45,000.00  
Time in years = (n)    40  
interest rate per year (i) =5% or   0.05  
      
Present Value of annuity formula =( P *(1-(1/(1+i)^n))/i)      
45000*(1-(1/(1+0.05)^40))/0.05      
$772,158.89      
      
So At time of retirement, after 25 years fund should be required =   $772,158.89  

Amount deposited per month (P)=   $6,000.00  
Time in months in 10 years (n)=10*12=   120  
interest rate per month (i) = 5℅/12=   0.004166666667  

Future value of annuity formula = P *{ (1+i)^n - 1 } / i      
6000*(((1+0.0041666667)^120)-1)/0.0041666667      
$931,693.68      
      
So At the end of 10 years after deposited amount accumulated=   $931,693.68  
Jewellery purchased at 10 years=   $50,000  
      
remaining amount=    $881,693.68  
      
So At the time of 10 years Amount accumulated is    $881,693.68  
while Amount required after 15 more years is just   $772,158.89  
also $881693.68 Amount will increased by interest in 15 years. So no more deposits is required to fund for retirement.      

Annual payment would be nil.