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
O $1.80

Answer 1

To find the difference between the balances of the two accounts at the end of 4 years, we need to calculate the balance of each account separately and then find the difference.

### Account I (Simple Interest)

The formula for simple interest is:
\[
I = P \times r \times t
\]
where:
- \( P = 1200 \) (the principal),
- \( r = 0.015 \) (the annual interest rate as a decimal),
- \( t = 4 \) (the time in years).

Calculating the interest for Account I:
\[
I = 1200 \times 0.015 \times 4 = 1200 \times 0.06 = 72
\]

The total balance in Account I after 4 years:
\[
\text{Total Balance I} = P + I = 1200 + 72 = 1272
\]

### Account II (Compound Interest)

The formula for compound interest is:
\[
A = P \times (1 + r)^t
\]
where:
- \( P = 1200 \),
- \( r = 0.015 \),
- \( t = 4 \).

Calculating the total balance in Account II:
\[
A = 1200 \times (1 + 0.015)^4 = 1200 \times (1.015)^4
\]

First, we calculate \( (1.015)^4 \):
\[
(1.015)^4 \approx 1.061364
\]

Now we find the total balance:
\[
A \approx 1200 \times 1.061364 \approx 1273.64
\]

### Difference between the two accounts

Now we can find the difference between the balances:
\[
\text{Difference} = \text{Total Balance II} - \text{Total Balance I} \approx 1273.64 - 1272 = 1.64
\]

Thus, the closest amount to the difference between the balances of the two accounts at the end of 4 years is:
\[
\boxed{1.64}
\]