Section 1
1. Section 1
1.17. Explore 2
Section 1: Simple and Compound Interest
Self-Check 1
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Julian downloads a compound interest calculator from the Internet to explore investment possibilities. He has $3000 to invest. At his bank, Julian can earn 3.6% compounded quarterly. How much will Julian have earned in interest if he leaves the money in this investment for 12 years?
The following variables have been identified from the problem. Use the compound interest formula to find the final amount of the investment (A).
P = $3000
r = 3.6% or 0.036 (This is the annual rate.)
n = 4 since the interest is added quarterly (4 times per year)
t = 12 years
In Self-Check 1, the annual interest of 3.6% was compounded quarterly—four times in one year. This means that the annual interest rate was split up over the four compounding periods during the year. The interest rate for each compounding period can be calculated according to the following chart.
| Interest | Number of Compounding Periods Per Year |
Interest Rate Per Compounding Period |
| Annually | 1 (once a year) | Annual Interest Rate |
| Semi-annually | 2 (every 6 months) |  |
| Quarterly | 4 (every 3 months) |  |
| Monthly | 12 |  |
The compounding period interest rate for Julian’s investment was the following:
