Question 1185409: 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(52775)   (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?
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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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