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 accounts at the end of 4 years?

$1.64

$72.00

$73.64

$1.80

Answer 1

To find the difference between the balances of the two accounts after 4 years, we will calculate the final balances of both accounts separately.

### Account I (Simple Interest)

The formula for calculating simple interest is:

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

where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial deposit).
- \(r\) is the annual interest rate (decimal).
- \(t\) is the time the money is invested for in years.

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

Calculating the balance:

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

### Account II (Compound Interest)

The formula for calculating compound interest is:

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

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

Calculating the balance:

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

We first calculate \(1.015^4\):

\[
1.015^4 \approx 1.061364
\]

Then we calculate \(A\):

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

### Difference between the balances

Now, we find the difference between the two accounts:

\[
\text{Difference} = \text{Balance of Account II} - \text{Balance of Account I}
\]

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

Thus, the amount closest to the difference between the balances of the two accounts at the end of 4 years is:

\[
\boxed{1.64}
\]