Online College Courses for Credit

FREE EDUCATIONAL RESOURCES PROVIDED by SOPHIA

Are you a student?
Free Professional Development
+

Savings and Loans

Rating:
(0)
Author: Danny Whittaker

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

No credit card required

29 Sophia partners guarantee credit transfer.

311 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 27 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

Tutorial

Compound Interest

Our next exponential application is compound interest.  If you invest money at an annual interest rate your money will grow exponentially by the formula:

where B is the final Balance

P is the starting balance

r is the annual interest rate (don't forget to divide a percent by 100)

n is the number of times you earn interest each year

t is the number of years the money is invested

So, if you invest \$100 at 8% annual interest compounded monthly for 50 years you will have:

We played around with different amounts of compounding and found that the more compoundings per year the more money you earn, but that the increase gets smaller and smaller with large values for n.

Explorations

Now that we've played with interest a bit, I want to know how long it will take to double an investment at different interest rates.  To simplify, take an initial investment of \$100.  Working with a monthly compounding and with different interest rates, how long will it take to double the money to \$200?  Work it out with at least five different interest rates.  See if you can come up with a rough rule for how long it will take for a different interest rate.