In Question 10, you figured out the periodic rate (interest per month) by dividing the APR by 12, the number of times the interest is being compounded in one month. In Question 11, to find the account balance after 24 months, you used 24 months in the exponent.
In the next problem, we want to develop a general formula to calculate the value of any CD.
Let
P = the principal,
r = the annual interest rate (APR) as a decimal,
n = the number of compounding periods in a year (1 for annual, 12 for monthly, 52 for weekly, etc.)
t = number of years.
So in the previous two questions, n = 12, since we were compounding monthly (12 times per year). Think about how you answered the last question: how did you find the interest rate per period? To find the value after 3 years, how did you figure out the number of months?
Question 12
Write a general formula that can be used to calculate the value of any CD, using the variables defined above (P, t, r, and n).
A =
Hint: If you get stuck, we'll provide some hints