Jeremy opened two saving accounts at the beginning of 2010, each with an initial deposit of $4,000. Account A earned simple interest, and account B earned interest that was compounded annually. By the end of 2012, which account earned more interest, and how much more interest did it earn?
A. Account A; $12.03
B. Account A; $47.25
C. Account B; $12.03
D. Account B; $47.25
Simple Interest: 4000 x 3.15% x 2 = 252
Compound Interest: 4000(1+3.15%)2(Squared 2) - 4000 = 255.969
255.969-252= 3.969
So my problem here is that I don't know what I did wrong and what I'm suppose to do to fix this and get the right answer because my teacher said that the right answer is C but I don't know why and I never got a chance to ask her.
Where did you get 3.15%?
By the end of 2012, that's 3 years, not 2.
A: 4000*.0315*3 = 378.00
B: 4000(1.0315^3-1) = 390.03
Looks like C to me.
If 3000 in an account interest 4% for 20 years
To determine which account earned more interest by the end of 2012, you need to compare the total interest earned by each account. Let's go through the calculations again:
For Account A, which earned simple interest:
Principal: $4,000
Interest Rate: 3.15%
Number of Years: 2
Simple Interest = Principal x Interest Rate x Number of Years
Simple Interest = $4,000 x 0.0315 x 2
Simple Interest = $252
For Account B, which earned compound interest:
Principal: $4,000
Interest Rate: 3.15%
Number of Years: 2
Compound Interest = Principal x (1 + Interest Rate)^Number of Years - Principal
Compound Interest = $4,000 x (1 + 0.0315)^2 - $4,000
Compound Interest ≈ $4,000 x (1.0635)^2 - $4,000
Compound Interest ≈ $4,000 x 1.13262225 - $4,000
Compound Interest ≈ $453.049 - $4,000
Compound Interest ≈ $453.049 - $4,000
Compound Interest ≈ $50.049
Now, you can see that the total interest earned by Account A is $252 and the total interest earned by Account B is $50.049.
Comparing the results, we find that Account A earned more interest than Account B. Therefore, the correct answer is option A: Account A earned $12.03 more interest.