Question

A deposit of 1200 is made into each of two back accounts. No additional deposits or withdrawals will be made for 4 years.

Account 1 earns 1.5% annual simple interest
Account 2 earns 1.5% interest compounded annually.

Whats the difference between the 2 accounts at the end of 4 years?

Answer 1

To find the difference between the two accounts at the end of 4 years, we'll calculate the total amount in each account and then determine the difference.

### Account 1: Simple Interest
The formula for simple interest is:

\[
A = P(1 + rt)
\]

Where:
- \(A\) is the total amount after time \(t\),
- \(P\) is the principal amount (initial deposit),
- \(r\) is the annual interest rate (as a decimal),
- \(t\) is the time in years.

For Account 1:
- \(P = 1200\)
- \(r = 0.015\) (1.5% as a decimal)
- \(t = 4\)

Plugging the values into the formula:

\[
A_1 = 1200(1 + 0.015 \times 4)
\]
\[
A_1 = 1200(1 + 0.06)
\]
\[
A_1 = 1200 \times 1.06
\]
\[
A_1 = 1272
\]

### Account 2: Compounded Interest
The formula for compound interest is:

\[
A = P(1 + r)^t
\]

For Account 2:
- \(P = 1200\)
- \(r = 0.015\)
- \(t = 4\)

Plugging the values into the formula:

\[
A_2 = 1200(1 + 0.015)^4
\]
\[
A_2 = 1200(1.015)^4
\]

Calculating \(1.015^4\):

\[
1.015^4 \approx 1.061364
\]

Now plugging this value back into the equation:

\[
A_2 \approx 1200 \times 1.061364
\]
\[
A_2 \approx 1273.64
\]

### Difference Between the Accounts
Now we find the difference between Account 2 and Account 1:

\[
\text{Difference} = A_2 - A_1 \approx 1273.64 - 1272 = 1.64
\]

Thus, the difference between the two accounts at the end of 4 years is approximately **$1.64**.