Savings Interest Calculator

What is Savings Interest?

Savings interest is the amount of money a bank or financial institution pays you for keeping your funds in a savings account. It's essentially a reward for allowing the bank to use your money for other purposes, such as lending to other customers.

The Savings Interest Formula

For savings accounts with regular deposits, we use the compound interest formula with periodic contributions:

\[A = P(1 + \frac{r}{n})^{nt} + M[\frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}}]\]

Where:

• \(A\) = Final amount
• \(P\) = Principal amount (initial deposit)
• \(r\) = Annual interest rate (in decimal form)
• \(n\) = Number of times interest is compounded per year
• \(t\) = Number of years
• \(M\) = Regular monthly deposit

Step-by-Step Savings Interest Calculation

1. Identify the principal amount (P), annual interest rate (r), compounding frequency (n), time period (t), and monthly deposit (M).
2. Convert the annual interest rate to a decimal (divide by 100).
3. Determine the total number of compounding periods (n * t).
4. Apply the formula to calculate the final amount (A).
5. Subtract the total deposits (initial principal + total monthly deposits) from the final amount to get the interest earned.

Example Calculation

Let's calculate the savings growth for an initial deposit of $5,000, monthly deposits of $100, an annual interest rate of 3%, compounded monthly, over 5 years:

1. \(P = \$5,000\), \(M = \$100\), \(r = 3\% = 0.03\), \(n = 12\) (monthly compounding), \(t = 5\) years
2. \(A = 5000(1 + \frac{0.03}{12})^{12 \times 5} + 100[\frac{(1 + \frac{0.03}{12})^{12 \times 5} - 1}{\frac{0.03}{12}}] = \$12,516.60\)
3. Total deposits = $5,000 + ($100 * 60 months) = $11,000
4. Interest earned = $12,516.60 - $11,000 = $1,516.60

Visual Representation

The green portion represents the total deposits ($11,000), and the blue portion represents the interest earned ($1,516.60).