EXPF01 Find the accumulated balance on $1000 placed at 6% interest for 5 years if the interest is compounded (a) annually, (b) quarterly or (c) monthly.

Solution:  If the interest on a principal amount is compounded once at the end of an interval the amount is A = P(1 + r) where r is the rate of return written as a decimal.  A one time 6% interest payment on $1000 would produce A = $1000(1 + 0.06) = $1060.  If this $1100 remained at the 6% and the interest compounded again at the end of the next interval and so on and so on for five years the amount would be A = $1000(1 + 0.06)⁵ = $1338.22. This is annual compounding.

Interest is usually stated on a yearly basis with specified compounding.

The phrase "6% compounded quarterly" means that the 6% is divided by 4 for the rate per interval (quarter) of 1.5% and there are 4 intervals per year.  In mathematical symbolism

would be the balance for an amount P placed at 6% interest for 4 quarters or 1 year.

The stated problem asks for the accumulated balance on $1000 after 5 years at 6% interest compounded quarterly so the appropriate formula is

If the compounding is done monthly then the rate has to be divided by 12 and the number of compoundings increased to       12 x 5 = 60.