SOLUTION: Chapter: Amount of Annuity You wish to purchase 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

Question 1162050: Chapter: Amount of Annuity
You wish to purchase 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?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Future value annuity formula:

A = future value
P = periodic contribution
r = annual interest rate
n = number of compounding periods per year
t = time (years)

Note those parameter definitions mean

r/n = periodic interest rate
1+r/n = periodic growth factor
nt = number of compounding periods

In this example,

A = 200,000
P = the unknown
r = 5% = .05
n = 2
t = 12
r/n = .025
1+r/n = 1.025
nt = 24

I'll let you get the practice in doing the calculations....

It's very easy to get ridiculous answers if you get decimal points or parentheses in the wrong place; make sure your answer makes sense.

You should get an answer of a little under $6200. That makes sense because not counting the interest $6200 every 6 months for 12 years is $6200*24 = $148,800; it's reasonable that the accrued interest will bring that up to the desired $200,000.

Answer by ikleyn(52824)   (Show Source): You can put this solution on YOUR website!
.

On Ordinary annuity and Annuity Due saving plans see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Annuity Due saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.

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