the discrete compounding formula is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is then number of time periods
in your problem, you are given:
f = what you want to find
p = 5000
r = 30% per year / 100 = .3 per year (percent / 100 = rate).
n = 3 years
if you compound annually, the formula becomes:
f = 5000 * (1 + .3) ^ 3 = 10985
if you compound quarterly, the formula becomes:
f = 5000 * (1 + .3 / 4) ^ (3 * 4) = 11908.898
if you compound monthly, the formula becomes:
f = 5000 * (1 + .3 / 12) ^ (3 * 12) = 12162.67658
if you compound continuously, a different formula is used.
that formula is f = p * e ^ (r * n)
f is the future value
p is the present value
e is the scientific constant of 2.718281828.......
r is the interest rate per time period
n is the number of time periods.
with this formula, you leave the time periods in terms of years.
it will make no difference what time periods and compounding periods you use, the answer will be the same.
most of the time you will just give it the interest rate per year and the number of years.
the reason is as follows:
r * n = .3 * 3 = .9 when giving it rate and time in terms of years.
r * n = .3 / 4 * 3 * 4 = .9 when giving it rate and time in terms of quarters.
r * n = .3 / 12 * 3 * 12 = .9 when giving it rate and time in terms of months.
in your problem, the formula becomes f = 5000 * e ^ (.3 * 3) = 12298.01556.
the more compounding periods per year, the higher the future value.
the highest is when you compound continuously.
this is apparent from the data.