How much less interest is earned at 6% simple interest for 5 years on a $10,000 investment than a 6% rate compounded daily for 5 years?
Interest on simple intereat part
= PRT
= 10000(.06)(5) = $3000
at 6% per annum compounded daily
amount = 10000(1 + .06/365)1825 = 13498.25
or $3498.25 in interest
so for the simple interest there would $498.25 less than the rate compounded daily.
To determine the difference in interest earned between simple interest and compound interest, we first need to calculate the interest earned in each scenario.
For simple interest, the formula is:
Interest = Principal x Rate x Time
Given:
Principal = $10,000
Rate = 6% = 0.06 (as a decimal)
Time = 5 years
Simple Interest = $10,000 x 0.06 x 5
Simple Interest = $3,000
Now, let's calculate the compound interest using the compound interest formula:
Compound Interest = Principal x (1 + Rate/Number of compounding periods)^(Number of compounding periods x Time)
In this case, we have daily compounding, so there are 365 compounding periods in a year.
Compound Interest = $10,000 x (1 + 0.06/365)^(365 x 5)
Compound Interest ≈ $10,000 x (1 + 0.000164)^(1825)
Compound Interest ≈ $10,000 x 1.34809
Compound Interest ≈ $13,480.90
Now we can calculate the difference in interest earned:
Difference in Interest = Compound Interest - Simple Interest
Difference in Interest = $13,480.90 - $3,000
Difference in Interest = $10,480.90
Therefore, the difference in interest earned is approximately $10,480.90 when comparing a 6% simple interest to a 6% compounded daily interest for 5 years.