FINANCE: ANNUITIES

Question

$500 are deposited into an account semiannually for six years at an interest rate of 5.5% compounded semiannually. How much is in the account at the end of the 6 years?  

 

PLEASE SHOW STEPS AND ANSWER

Answer 1

What's different about this problem is that it doesn't use the ordinary annuity calculation; rather, it uses the FV of Annuity Due calculation, which is:

 

FV_{A Due} = {[PMT (1 + r)ⁿ - 1] / [r)}  * (1 + r)    | Note:  Don't forget semi-annual means 5.5 ÷ 2 = 2.75

 

Which gives us:

 

{[500 * (1.0275)¹² / 0.0275]} * (1.0275)

 

So, [(673.86)/ (0.0275)] * (1.0275)

 

Which gives us:  $6,996  * 1.0275 = $7,188.46