SOLUTION: You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 mont

Question 1185415: You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 months, so that you will have $200,000 at the time of your last deposit? (Hint: You need to find the value for "a". )

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
You wish to purchased a house for $200,000 in 12 years.
You can invest your money at 5% compounded semiannually.
How much do you need to invest every 6 months, starting in 6 months,
so that you will have $200,000 at the time of your last deposit?
~~~~~~~~~~~~~~~~~~~~~~~~~

This problem is about ordinary annuity.
They want you to determine regular semi-annual deposits to get
$200,000 in 12 years, depositing at 5% compounded semiannually.


The general formula is 

    FV = ,    


where  FV is the future value of the account;  P is the semi-annual deposit value; 
r is the semi-annual effective rate presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 2, in this case).


From this formula, you get for the semi-annual deposit value 


    P = .     (1)


Under the given conditions, FV = $200,000;  r = 0.05/2 = 0.025;  n = 12*2 = 24.  
So, according to the formula (1), you get for the semi-annual deposit value


    P =  = 6182.57  (rounded to closest greater cent).


Answer.  The necessary semi-annual deposit value is $6182.57.

Solved.

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