Question 1188488: Discuss the importance of the number of times interest is compounded annually when borrowing from the bank
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the growth factor per year is equal to (1 + r/c) ^ n * x
r is the nominal growth rate per year (not compounded).
c is the number of compounding periods per year.
as an example, assume the nominal growth rate per year is 24%.
wen you compound only 1 time per year, the growth factor per year becomes (1 + .24/1) ^ (1*1) = 1.24.
the effective interest rate per year = (1.24 - 1) * 100 = 24%.
when you compound 4 times a year, the growth factor per year becomes (1 + .24/4) ^ (4 * 1) = 1.26247696.
the effective interest rate per year becomes (1.26247696 - 1) * 100 = 26.247696%.
when you compound 12 times a year, the growth factor per year becomes (1 + .24/12) ^ 12 = 1.268241795.
the effective interest rate per year becomes (1.268241795 - 1) * 100 = 26.8241795%.
the effective interest rate per year gets higher as the number of compounding periods per year gets higher.
the effect of this becomes greater as the number of years of inveetment gets higher.
example:
you invest 1000 at 24% interest rate per year.
in 20 years, without compounding, your money is worth 1000 * (1 + .24) ^ 20 = 73,864.14979.
in 20 years, with monthly compounding, your money is worth 1000 * (1 + .24/12) ^ (20 * 12) = 115,888.7352.
let me know if you have any questions.
theo
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