Short-term savings refers to money set aside for near-future expenses or goals, typically within a timeframe of a few months to a couple of years. These savings are often kept in easily accessible accounts like high-yield savings accounts, money market accounts, or short-term certificates of deposit (CDs). The primary goal of short-term savings is to balance liquidity with modest growth through interest earnings.

The formula used to calculate the growth of short-term savings with compound interest is:

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

- Identify the principal amount (P), annual interest rate (r), compounding frequency (n), and term (t).
- Convert the annual interest rate to decimal form (divide by 100).
- Divide the annual rate by the compounding frequency to get the periodic rate.
- Convert the term to years if given in months (divide by 12).
- Multiply the compounding frequency by the number of years to get the total number of compounding periods.
- Apply these values to the compound interest formula.
- Calculate the final amount (A).
- Subtract the principal from the final amount to determine the interest earned.

Let's calculate the growth of a short-term savings account with an initial deposit of $5,000, an annual interest rate of 2%, compounded monthly, over 6 months:

- \(P = \$5,000\), \(r = 2\% = 0.02\), \(n = 12\) (monthly compounding), \(t = 6/12 = 0.5\) years
- Periodic rate = \(0.02 \div 12 = 0.001667\)
- Total compounding periods = \(12 \times 0.5 = 6\)
- \(A = 5000(1 + 0.001667)^{6} = \$5,050.15\)
- Interest earned = \$5,050.15 - \$5,000 = \$50.15

The green portion represents the principal ($5,000), and the blue portion represents the interest earned ($50.15) over the 6-month period.

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