Question 1112944: Hellen needs 20 000 in three years time.what is the least amount that she should deposit now into an account that offers an annual interest rate of 15%,compounded every 3 months,to have the required amount by then? The answer to the nearest rand is?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = p * (1 + r) ^ n
f = future value
p = present value
r = interest rate per time period
n = number of time periods.
in your problem.
f = 20,000
r = 15% per year compounded quarterly (every 3 months)
n = 3 years.
use interest rate as a decimal rather than percent.
15% = .15
divide interest rate by number of compounding periods per year to get:
r = .15/4 = .0375 per quarter.
multiply number of years by 4 to get number of quarters.
3 * 4 = 12 quarters.
f = p * (1 + r) ^ n becomes:
20,000 = p * (1 + .0375) ^ 12
solve for p to get:
p = (20,000 / (1 + .0375) ^ 12).
this results in p = 12,857.97956
that's how much needs to be invested today in order to have 20,000 in 3 years at 15% per year compounded quarterly.
12,857.97956 * (1 + .0375) ^ 12 = 20,000
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