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Question 643165: I need to figure out how much to invest at 12% compounded semi-annually over 4 years to end up with $28,000. Is there a formula for this? I have tables for annual interest compounding but nothing to help with semi-annual compounding.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! when you compound, you divide the interest rate by the compounding period and you multiply the number of time periods by the compounding period.
in your problem, you have 28,000 invested at 12% compounded semi-annually for 4 years.
the interest rate is equal to 12/2 = 6% per semi-annual period.
the number of semi-annual periods is equal to 4*2 = 8.
use your compounding table at 6% for 8 periods and you should get your answer.
the formula for compounding is:
f = p * (1+(i/c))^(y*c)
f = future value
p = present value
i = annual interest rate (this equals % divided by 100).
c = number of compounding periods per year.
y = number of years.
c = 2 because you are compounding 2 times a year (semi-annual)
i = .12 / 2 = .06
y*c = 4*2 = 8
p = 28000
formula becomes:
f = 28000 * 1.06^8
your answer should be:
f = 28,000 * (1.06)^8 which is equal to 44627.75 rounded to 2 decimal places.
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