Question

Future Value of an Annuity for Various Compounding Periods

Find the future values of the following ordinary annuities:

1. FV of $200 paid each 6 months for 9 years at a nominal rate of 12%, compounded semiannually. Round your answer to the nearest cent.
   $   
   
2. FV of $100 paid each 3 months for 9 years at a nominal rate of 12%, compounded quarterly. Round your answer to the nearest cent.
   $   

Answer 1

Future Value of Annuity P [{(1+r)" - 1}/ r] Where P Periodic Payment r Rate for the Period n= Number of Period Accordingly, FV of $ 200 Paid each 6 months for 9 years at a nominal rate of 12 % compounded Semi-annually. (a). P Periodic Payment $ 200. r Rate for the Period (12/2)= 6% or 0.06 n= Number of Period (9 Years 2) 18 Periods Future Value of Annuity P* [{(1+r)"- 1}/r] Future Value of Annuity $200* [{(1+0.06) -1}/0.06] 18 18 = $200 [{1.06)-1}/0.06 - $ 200* [{2.8543 1}/0.06] = $200 [1.8543 /0.06] = $ 200 30.905 = $6,181 answer FV of $ 100 Paid each 3 months for 9 years at a nominal rate of 12 % compounded quarterly (b) P Periodic Payment $ 100. r Rate for the Period (12/4) 3% or 0.03 n Number of Period (9 Years* 4 quarter)= 36 Periods Future Value of Annuity P * [{(1+r)" - 1}/ r] Future Value of Annuity $100 * [{(1+0.03)3 - 1 }/0.03] 36 = $ 100 [(1.03)-1}/ 0.03] = $100 [2.8983 - 1}/0.03] $100 [1.8983 /0.03] $100 63.2767 =$6328 answer.

Answrs are rounded off to nearest dollar.