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 I| earns 1.5% interest compounded annually.
Which amount is closest to the difference between the balances of the two accounts at the end of 4 years?
$1.64
$72.00
$73.64
$1.80

Answer 1

To determine the difference between the balances of the two accounts after 4 years, we need to calculate the balance of each account separately.

**For Account I (Simple Interest):**
The formula for calculating the balance with simple interest is:

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

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

Given:
- \( P = 1200 \)
- \( r = 0.015 \)
- \( t = 4 \)

Substituting the values into the formula:

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

**For Account II (Compound Interest):**
The formula for calculating the balance with compound interest is:

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

Using the same values for \( P \), \( r \), and \( t \):

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

Now calculating \( (1.015)^4 \):

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

Now substituting back into the compound interest formula:

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

**Calculating the Difference:**
Now we find the difference between the balances:

\[
\text{Difference} = \text{Balance of Account II} - \text{Balance of Account I}
\]
\[
\text{Difference} = 1273.64 - 1272
\]
\[
\text{Difference} \approx 1.64
\]

Thus, the amount closest to the difference between the balances of the two accounts at the end of 4 years is **$1.64**.

The answer is **$1.64**.