Question

51. You have your choice of two investment accounts. Investment A is a 10 year annuity that features end of month $1,145 payments and has an interest rate of 7% compounded monthly. Investment B is an annually compounded lump – sum investment with an interest rate of 9%, also good for 10 years. How much money would you need to invest in B today for it to be worth as much as Investment A 10 years from now.

Answer 1

Monthly payment=   1145  
Time (n) in months 10*12=    120  
interest rate is 7% compounded monthly. Monthly interest rate = 7%/12=   0.005833333333  
Future value of annuity formula = P *((1+r)^n - 1) / r       
Investment A future value is:      
1145*(((1+0.00583333333)^120)-1)/0.0058333333      
198182.1045      
      
Investment B Required future value=   198182.1045  
Time (n) in years =   10  
Interest rate annual = 9% or   0.09  
      
Investment made to be required today is Present value.      
Present value of future value formula= Future value/(1+i)^n      
198182.1045/(1+0.09)^10      
83714.26268      
      
So money need to invest in B today is   $83,714.26