Question

A deposit of $1,200 is made into each of two bank accounts. No additional deposits or withdrawals will be made for 4 years.

Account I earns 1.5% annual simple interest.

Account II earns 1.5% interest compounded annually.

Which amount is closest to the difference between the balances of the two acco

Answer 1

To find the difference between the balances of the two accounts after 4 years, we will calculate the final amount in each account and then find the difference.

### Account I (Simple Interest)

The formula for calculating the amount with simple interest is:

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

where:
- \( A \) is the final amount,
- \( P \) is the principal amount (initial deposit),
- \( r \) is the annual interest rate (in decimal),
- \( t \) is the time in years.

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

Plugging in these values:

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

### Account II (Compound Interest)

The formula for calculating the amount with compound interest is:

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

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

Plugging in these values:

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

Calculating \( (1.015)^4 \):

\[
(1.015)^4 \approx 1.061364
\]

Now, substituting back:

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

### Finding the Difference

Now, we calculate the difference between the two accounts:

\[
\text{Difference} = A_{\text{Compound}} - A_{\text{Simple}}
\]
\[
\text{Difference} \approx 1273.64 - 1272
\]
\[
\text{Difference} \approx 1.64
\]

Thus, the amount closest to the difference between the balances of the two accounts is approximately **$1.64**.