Question 1138724: You invest $10 000 for 9 years at 12%p.a, how much money will you get back if interest is compounded:
a) yearly
b) half- yearly
c)quartely
d) monthly
e) continuously
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the investment is 10,000 for 9 years at 12% per year.
the formula to use is f = p * (1 + r) ^ n for discrete compounding.
the formula to use is f = p * e^(r * t) for continuous compounding.
the greater the number of compounding periods per year, the larger the future value, up to continuous compounding, which is as high as you can go.
with annual compounding, the formula becomes:
f = 10000 * (1 + .12) ^ 9 = 27,730.79.
all answers are rounded to the nearest penny.
with semi-annual compounding, r = .12/2 and n = 9 * 2 and the formula becomes:
f = 10000 * (1 + .12/2) ^ (9 * 2) = 28,543.39.
with quarterly compounding, r = .12/4 and n = 9 * 4 and the formula becomes:
f = 10000 * (1 + .12/4) ^ (9 * 4) = 28,982.78.
with monthly compounding, r = .12/12 and n = 9 * 12 and the formula becomes:
f = 10000 * (1 + .12/12) ^ (9 * 12) = 29,289.26.
with continuous compounding, r = .12 and t = 9 and the formula becomes:
f = 10000 * e^(.09 * 9) = 29,446.80.
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