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How to Calculate Simple Interest for $2000 Invested at 5% for 8 Months
Mathematics
Grade 7 (Junior High School)
Question Content
$2,000 is invested at 5% interest for 8 months. Find the interest.
Correct Answer
$66.67
Detailed Solution Steps
1
Step 1: Identify the values needed for simple interest formula. Principal (P) = $2000, annual interest rate (r) = 5% = 0.05, time (t) must be in years. Since the time given is 8 months, convert it to years: t = 8/12 = 2/3 ≈ 0.6667 years.
2
Step 2: Use the simple interest formula I = P × r × t, where I is the interest earned.
3
Step 3: Substitute the values into the formula: I = 2000 × 0.05 × (2/3).
4
Step 4: Calculate the product: 2000 × 0.05 = 100; then 100 × (2/3) ≈ 66.67.
Knowledge Points Involved
1
Simple Interest Formula
The formula for simple interest is I = P×r×t, where I = interest earned, P = initial principal amount, r = annual interest rate (expressed as a decimal), t = time the money is invested/borrowed in years. It is used for calculating interest on short-term investments or loans where interest is only calculated on the original principal.
2
Unit Conversion for Time in Interest Calculations
Interest rates are typically given on an annual basis, so any time period given in months, weeks, or days must be converted to a fraction of a year. For months, divide the number of months by 12 to get the time in years, as there are 12 months in a year.
3
Percent to Decimal Conversion
To use a percentage in mathematical calculations, convert it to a decimal by dividing the percentage value by 100. For example, 5% becomes 0.05, which is necessary for substituting into interest formulas.
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