
Chapter 4.2®  Compounding Interest Homework Problem & Time Value of Money Continued  Future Value Formula, Growth of $100 & Future Value Comparisons
From the introduction to time value of money (part 4.1), we can derive a formula, which will be the future value of $1 invested for t periods at a rate of r per period. The equation is:
The expression (1 + r)^{t} is sometimes referred to as the future value interest factor for $1 invested at r percent for t periods of time. Let’s use this future value formula to derive the original $121 at the end of the 2nd year.
The table below shows the growth of $100 each year at 10% interest. Each year, the interest earned is equal to the beginning amount multiplied by the interest rate (10%). How much of this $161.05 is simple interest, and how much of it is compounding interest? Well $100 x 0.10 = $10 per year, so in 5 years, the total simple interest is 5 years x $10 = $50. Thus, we can calculate the compounding interest by subtracting $161.05  $150 = $11.05
Compound Interest Homework Problem Consider
you found an investment that pays 15% annual interest, which sounds fantastic
to you! This makes you invest $1000 in to it, how much will you have in
3 years? How much will you have in 7 years? And at the end of 7 years,
how much interest will you have earned, and how much of it will be compounding
interest?
You invested $1000 x 15% = $150 simple interest each year, thus total simple interest in 7 years = $150 x 7 = $1,050

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