4.6.1: Preparation 4.6

In Collaboration 4.5, you learned how to calculate the accumulated amount (A) of a certificate of deposit (CD), when compounding occurs annually. In this assignment, you will learn a more general method of compounding for which compounding periods may be of various durations. In addition, you will connect the exponential mathematics of compounding to related applications (e.g., automobile depreciation). More importantly, you will see the effect of different compounding factors.

(1) For the given compounding periods, fill in the “Periods per Year” column.

Example: Let’s say you invest $1,000 in a one-year CD, advertised with an annual percentage rate (APR) of 6%, where compounding occurs monthly.

We have an APR of 6% per year, and because the compounding occurs monthly, we need to determine the monthly interest rate (also called the periodic rate).

We can do this by simply dividing the APR expressed as a decimal (6% expressed as a decimal is 0.06) by the number of compounding periods. In this example, the number of compounding periods is 12. So, the monthly interest rate is \(\dfrac{0.06}{12}\) = 0.005.

We can then use this monthly rate to calculate how much our initial investment will increase by month to month.

1 month: $1,000 + $1,000 ⨉ 0.005 = $1,000(1 + 0.005) = $1,000 ⨉ 1.005 = $1,005

2 months: ($1,000 ⨉ 1.005)1.005 = $1,000(1.005)2 = $1,010.03 (rounded up)

3 months: ($1,000 ⨉ 1.0052)1.005 = $1,000(1.005)3 = $1,015.08

(2) If you were to invest $2,000 over 1 year at 6% interest compounded monthly, what would your balance be after one month?

(3) If you were to invest $4,000 at 6% interest compounded monthly, what would your balance be after one month?

Collaboration 4.6 builds on the concepts from Collaboration 4.5, so the prerequisite skills listed below were all covered in the previous sections of this assignment.

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