An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made, what will happen to the interest?
An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made, what will happen to the interest?
The Correct Answer and Explanation is:
If no deposits or withdrawals are made, the account will earn interest annually at a rate of 2%, meaning the balance will gradually grow over time due to compound interest. The interest will continue to be calculated based on the growing balance each year.
Explanation
An account with a $250 balance that accrues 2% annual interest is earning compound interest if the interest is added to the principal each year. This means that each year’s interest is calculated not just on the initial $250, but also on any interest already earned.
Let’s look at the first few years:
- Year 1:
Interest = $250 × 2% = $5
New balance = $250 + $5 = $255 - Year 2:
Interest = $255 × 2% = $5.10
New balance = $255 + $5.10 = $260.10 - Year 3:
Interest = $260.10 × 2% ≈ $5.20
New balance ≈ $265.30
This process continues each year. The interest earned increases slightly each time because it is being calculated on a growing balance. This is the essence of compound interest: interest earning interest.
If you leave the account untouched for many years, the balance will grow steadily, even without any new deposits. Although a 2% annual interest rate is relatively low, over long periods (e.g., 10, 20, or 30 years), the effects of compounding can become significant.
The formula for compound interest is:
A = P(1 + r)^t,
where:
- A = future value
- P = principal ($250)
- r = annual interest rate (0.02)
- t = number of years
This formula shows how the balance increases exponentially over time, not linearly. So, if no transactions are made, the account balance will grow slowly but continuously, solely due to the compounding of the 2% annual interest
.