Question

You are 40 now and at age 60 you wish to buy a 20 year annuity that makes monthly payments of $3,500 which earns a rate of 1% per

month.

a. You have $15,000 to invest now to save up and buy that annuity. Would annual interest rate would you need to earn to achieve

your goal?

b.How many periods will it take money to double at rate of 10% per period (rounded to the nearest period)?

Answer 1

a  
amount per month (P)=   3500
interest rate per month (i)=    1%
total months (n)= 20*12=   240
Value of Annuity at year 20 (age 60) shall be calculated by Present Value of Annuity Formula   
Present Value of ordinary annuity formula = (P *(1-(1/(1+i)^n))/i)  
3500*(1-(1/(1+1%)^240))/1%  
317,867.96  
  
This is required future value of Investment =   317,867.96
Present value of savings   15000
Number of years (n)=   20
  
Annual Return Formula = ((Future Value/Present Value)^(1/n))-1  
((317867.96/15000)^(1/20))-1  
0.1650   or 16.50%
  
  
So 16.50% annual rate is required to achieve the goal  
  
b. interest rate =   10%
As per rule 72, time needed to double the Investment = 72/Rate  
72/10=   7.2 years
So 7.2 years is required to double the Investment