Question 1112944
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