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Examine the compound interest formula. Determine the variables for each account.
Examine the benefits and drawbacks of the accounts under three topics which are time, deposit, and interest.
| Amount ($) | Interest ($) | |
|---|---|---|
| CD Specials | 1592.68 | 92.68 |
| Anytown Community Account | 2123.23 | 123.23 |
See solution.
We will begin by analyzing the compound interest formula.
A= P(1+r/n)^(n t)
The components of the formula can be described as shown below.
A:& amount in the account after t years
P:& initial amount
r:& annual rate written as a decimal
n:& number of periods
t:& number of years
| CD Specials | Anytown Community Bank | |
|---|---|---|
| Initial Amount ($) | P_1=1500 | P_2=2000 |
| Annual Rate | r_1=0.02 | r_2=0.03 |
| Number of Years | t_1=3 | t_2=5 |
Now, we can continue by finding the amount in CD Specials at the end of its term. Notice that the interest is compounded monthly, so the number of periods will be 12.
The amount is about $1592.68. But subtracting the initial amount from the final amount, the amount of interest can be found. 1592.68-1500=92.68 Therefore, the amount of interest is about $92.68. Proceeding in the same way, we can find the amount in Anytown Community Bank.
| P | r | n | t | P(1+r/n)^(nt) | A | |
|---|---|---|---|---|---|---|
| CD Specials | 1500 | 0.02 | 12 | 3 | 1500(1+0.02/12)^(12( 3)) | 1592.68 |
| Anytown Community Account | 2000 | 0.03 | 12 | 5 | 2000(1+0.03/12)^(12( 5)) | 2123.23 |
Next, we will find the amount of interest.
| A | P | Interest | |
|---|---|---|---|
| CD Specials | 1592.68 | 1500 | 1592.68-1500=92.68 |
| Anytown Community Account | 2123.23 | 2000 | 2123.23-2000=123.23 |
We can examine the benefits and drawbacks of the accounts under three topics which are time, deposit, and interest.