Question

Your bank offers 3 percent annual interest on savings deposits. If you deposit \(\$ 560\) today, how much interest will you have earned at the end of one year?

Short answer

You will earn $16.80 in interest.

Step-by-step solution

Understanding the Interest Rate

The bank offers an interest rate of 3% per annum. This means that for every dollar you deposit, you earn 0.03 dollars in interest over the course of a year.

Calculating Interest Earned

To find out how much interest you will earn on a deposit of \(\$560\), use the formula for simple interest: \[\text{Interest} = \text{Principal} \times \text{Interest rate}\]Substituting the given values:\[\text{Interest} = 560 \times 0.03\]

Performing the Calculation

Calculate the interest using the values from the previous step.\[\text{Interest} = 560 \times 0.03 = 16.8\]

Key concepts

Interest Rate

An interest rate is the percentage at which you earn money on your deposited savings, or sometimes owe money when you borrow from a financial institution. In our exercise, the bank offers a 3% annual interest rate on savings deposits. This means that for every dollar deposited into a savings account, the bank gives you an additional 3 cents by the end of the year. An interest rate can serve different purposes, whether encouraging people to save money or make borrowing more affordable. Interest rates can be represented in different forms, such as percentages per annum (yearly), monthly, or even daily. For most savings accounts, an annual interest rate is typical. This allows for easy planning and projection of how much you can expect to earn on your savings over the course of a year.

Annual Interest

Annual interest refers to the amount of money earned or paid over one full year based on the principal amount and the annual interest rate. For savings accounts, this is the interest earned on the amount deposited. The amount of annual interest can be easily calculated using the formula:\[ \text{Interest} = \text{Principal} \times \text{Interest Rate} \]In this formula, "Principal" refers to the initial amount deposited, and "Interest Rate" is the annual percentage rate offered. For the exercise, the principal is \(560, and the interest rate provided by the bank is 3% or 0.03.Simplifying our calculation:- Multiply the principal \)560 by the interest rate 0.03- You get 16.8, which means $16.80 will be earned in interest for that year.

Savings Deposits

Savings deposits are sums of money placed in a savings account at a financial institution, like a bank, intended to be saved rather than spent. These accounts usually accrue interest over time, encouraging the saver to save more funds by earning returns on their deposit. When you make a savings deposit, it generally has the following benefits: - Safe storage of funds with banks ensuring secure protection - Opportunity to earn interest over time - Easy access to funds compared to longer-term investments In our exercise, you're making a savings deposit of $560. Over the course of a year, since the bank offers a 3% annual interest rate, this deposit will yield $16.80 in simple interest. Therefore, at the end of one year, your total amount in the savings account will be $576.80, reflecting both the original deposit and the interest earned. These characteristics make savings deposits an attractive, low-risk option for those aiming to grow their funds gradually while maintaining easy access to their money at any given time.