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 1185410: 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 Theo(13342) (Show Source): You can put this solution on YOUR website!
you can use a financial calculator to solve this.

your inputs are shown below.

your output is shown below.

you can also solve this by formula.

the formula is:

a = (f*r)/((1+r)^n-1)
a is the annuity.
f is the future amount.
r is the interest rate per time period.
n is the number of time periods.

for your problem.

f = 200,000 (without the comma.
r is the interest rate per time period = .05/2 = .025 per semi-annual time period.
n is the number of time periods = 12 * 2 = 24 semi-annual time periods.

a = (f*r)/((1+r)^n-1) becomes:

a = (200000*.025)/((1+.025)^24-1) = 6182.564072.

this is the same as what the calculator tells you when rounded to 2 decimal places.

the calculator says the payment at the end of each semi-annual period is equal to 6182.56.
https://arachnoid.com/finance/index.html
the calculator can be found at https://arachnoid.com/finance/index.html

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