If the principal P = $900, the rate r = 4 1/2, and time t = 1 year, find the following: What is the amount of interest? What is the future value?
Interest for the first year is the principal, P=$900 multiplied by the rate of interest, r=0.045, multiplied by the number of periods, n=1.
So interest
I=$900*0.045*1=$40.5
The future value is the sum of the interest and the principal.
Note that in this case (n=1), the interest is the same whether it is simple or compound. In general, the question should specify whether it is simple interest or compound interest. In the latter case, the compounding period should also be specified (yearly, quarterly, monthly, etc.)
To find the amount of interest and the future value, we can use the formulas:
Amount of Interest = Principal * Rate * Time
Future Value = Principal + Amount of Interest
Let's plug in the given values:
Principal (P) = $900
Rate (r) = 4 1/2 (4.5% as a decimal)
Time (t) = 1 year
Converting the rate to a decimal:
4 1/2 = 4 + 1/2 = 4.5
4.5% = 4.5/100 = 0.045
Now we can calculate the amount of interest:
Amount of Interest = $900 * 0.045 * 1 = $40.50
And the future value:
Future Value = $900 + $40.50 = $940.50
Therefore, the amount of interest is $40.50, and the future value is $940.50.