Treasure Mountain International School in Park City, Utah, is a public middle school interested in raising money for next year's Sundance Film Festival. If the school raises $2,989 and invests it for 1 year at 3% interest compounded annually, what is the APY earned? Please help!
Assuming the investment is placed for exactly one year, then the future value is
FV=Principal*(1+i)
=2989(1+0.03)
= $3078.67
To calculate the APY (Annual Percentage Yield) earned on an investment, we can use the formula:
APY = (1 + r/n)^n - 1
Where:
r = effective annual interest rate (in decimal form)
n = number of compounding periods per year
In this case, the investment is made for 1 year at 3% interest compounded annually.
Step 1: Convert the interest rate to decimal form:
3% = 0.03
Step 2: Plug the values into the formula:
APY = (1 + 0.03/1)^1 - 1
APY = (1 + 0.03)^1 - 1
APY = (1.03)^1 - 1
Step 3: Calculate the APY:
APY = 1.03 - 1
APY = 0.03
Therefore, the APY earned on the investment is 0.03, or 3%.
To calculate the APY (Annual Percentage Yield) earned on an investment with compound interest, you need to use the formula:
APY = (1 + r/n)^n - 1
where:
- r is the interest rate as a decimal (in this case, 3% or 0.03)
- n is the number of times the interest is compounded per year (in this case, annually, so n = 1)
Let's plug in the values and solve:
APY = (1 + 0.03/1)^1 - 1
= (1 + 0.03)^1 - 1
= 1.03 - 1
= 0.03 or 3%
So the APY earned on the investment will be 3%.
In this case, the APY is the same as the interest rate (3%) because the interest is compounded annually. But if the interest was compounded more frequently (e.g., quarterly or monthly), the APY could be higher due to the effect of compounding.