Question

Example 1: Calculating Annual and Monthly Payments
Your client desires a balance of $1 million in a retirement account by
the end of 20 years, and you project an annual return of 6% on
investments. Determine the required annual contribution at the
end of each fiscal year to reach this goal. Example 2: Calculating Annual and Monthly Payments Your client is buying a home for $300,000 and would like to determine the amont of the monthly mortgage payments. The client can obtain financing for $240,000 over a 30-year period with a fixed annual interest rate of 4%.

Answer 1

Note: The contribution is made at the end of each fiscal year and we assume that 6% interest rate is compounded annually.              
              
To calculate the annual contribution we use the following formula -               
Balance(Y) = P(1+r)^y + [c((1+r)^y-1))/r]              
              
Where              
y= no of years = 20              
r= Rate of return = 6/100=0.06              
P= Principle Amount = Nil              
c= Annual Contribution              
              
Putting values in the above formula we get,              
              
10,00,000 = 0(1+0.06)^20 +[ c((1+0.06)^20-1))/0.06]              
Solving the above equation we get              
10,00,000 = 0 + c[ (3.207-1)/0.06]              
c= $ 27,185 (approximately)              
              
Hence monthly contribution = 27185/12= $ 2265.42              

Calculation of Monthly Mortgage payments is done using the following formula          
          
Monthly Mortgage payments =[P*r*(1+r)^n]/(1+r)^n-1          
where P= Mortgage Loan           
r= rate per month          
n=number of monthly instalments          
          
Putting Values we get -          
Monthly Mortgage = 240000*0.04/12*[(1+0.04/12)^360]/(1+0.04/12)^360-1          
Monthly Mortgage = $1145.8          

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