Margaret Hillman invested $3,000 at 1%
compounded quarterly for one year. Find the future value and the interest earned for the year.
V = Vo(1+r)^n.
r = 0.01/4 = 0.0025 = Quarterly % rate expressed as a decimal.
n = 4 Compounding period.
V = (3000(1.0025)^4 =
Int. = V - Vo.
Well, investing $3,000 at 1% compounded quarterly is quite the thrilling adventure! Now let's do some math and see where this rollercoaster ride takes us.
To find the future value, we begin by calculating the total number of compounding periods in a year. Since interest is compounded quarterly, there are 4 periods in a year.
Next, we plug in the numbers into the formula for compound interest:
Future Value = Principal Amount × (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods × Time)
Applying this formula to our situation, we get:
Future Value = $3,000 × (1 + (0.01 / 4))^(4 × 1)
Calculating this out, we find the future value to be approximately $3,030.30.
Now, let's move on to the interest earned. To determine this, we subtract the principal amount from the future value:
Interest Earned = Future Value - Principal Amount
So, the interest earned in this amusing investment adventure comes out to be around $30.30.
Remember, investing can be a wild ride, so buckle up and enjoy the financial rollercoaster!
To find the future value and interest earned for the investment, we can use the formula for compound interest:
Future Value = Principal * (1 + (Rate / n))^(n * t)
where:
Principal = $3,000 (initial investment)
Rate = 1% (annual interest rate)
n = 4 (compounding periods per year, since it is compounded quarterly)
t = 1 year (investment duration)
Let's calculate the future value first:
Future Value = $3,000 * (1 + (0.01 / 4))^(4 * 1)
= $3,000 * (1 + 0.0025)^(4)
= $3,000 * (1.0025)^(4)
= $3,000 * 1.010050625
≈ $3,030.15
Therefore, the future value of the investment after one year is approximately $3,030.15.
To find the interest earned, we need to subtract the initial investment from the future value:
Interest Earned = Future Value - Principal
= $3,030.15 - $3,000
≈ $30.15
Therefore, the interest earned for the year is approximately $30.15.
To find the future value and the interest earned for the year, we can use the formula for compound interest:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods)) ^ (Number of Compounding Periods * Number of Years)
In this case, the principal amount is $3,000, the interest rate is 1% (or 0.01 as a decimal), and the compounding period is quarterly, which means there are 4 compounding periods in a year.
Let's calculate the future value first:
Future Value = $3,000 * (1 + (0.01 / 4)) ^ (4 * 1)
Future Value = $3,000 * (1.0025) ^ 4
Future Value = $3,000 * 1.010050625
Future Value = $3,030.15 (rounded to two decimal places)
Now, let's find the interest earned:
Interest Earned = Future Value - Principal
Interest Earned = $3,030.15 - $3,000
Interest Earned = $30.15
Therefore, the future value of the investment is $3,030.15, and the interest earned for the year is $30.15.