# Find the accumulated value of an investment fund

Find the accumulated value at the end of six years of an investment fund in which \$100 is deposited at the beginning of each quarter for the first three years and \$50 is deposited at the beginning of each quarter for the second three years, if the fund earns 6% convertible monthly.

I need help understanding the solution.

Where is the exponent 3 coming from? The quarterly interest rate equivalent to 6% convertible monthly is $$(1.005)^3 – 1 = 0.015075$$

I am not sure now how to find the accumulated value at the end of six years.

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When you ask where the exponent 3 is coming from, are you talking about the following equation? Note that there are three months in a quarter. –  Trevor Wilson Feb 27 '13 at 21:39
The exponent $3$ comes because there are three months in a quarter. The $6\%$ per year equates to $0.5\%$ per month. After three months this has compounded to $1.005^3$