An investment of $\$24,\!000$ is made in a government bond that will pay $1\%$ bi-monthly interest (meaning that the investment will increase by $1\%$ every two months). At the end of five years, what is the total number of dollars in this investment? Express your answer to the nearest whole number.

Guest Aug 6, 2018

#1**+1 **

This is a rather unusual question that it is very "unrealistic" in the sense that you would never expect the U.S. government to pay you 1% extra EACH 2-month period for 5 years or a total of 30% compounded bi-monthly!!.

I do realize that this is just an exercise for students to learn about "exponential growth". But, it also cannot easily be summed up as Geometric Series since there is no common ratio shared between them.

The interest rate increases as follows every 2 months:

1.01, 1.02, 1.03, 1.04.........and so on for 30 2-month periods that end in: 1.28, 1.29, 1.30. Now, you could multiply all these 30 numbers together and then multiply the result by $24,000! But that is rather cumbersome and awkward. But there is shortcut that would simplify things a lot:

So, instead of multiplying 1.01 x 1.02 x 1.03.......1.28 x 1.29 x 1.30, one can do this instead: multiply all of them by 100 and then use the "permutations formula", nPr, to compute them as follows:

**[130 ****nPr**** 30] / 100^30 =69.2930218852..... x $24,000 =$1,663,033 - which is what you will have at end of 5 years!!!!.**

Guest Aug 7, 2018