Compute the amount of compound interest earned in 1 year for an investment of $1,000,000 with a nominal interest rate of 8% compounded quarterly. Then Compute the Annual Percentage Yield (APY) for the investment in the previous question. (Round APY to the nearest hundredths of a percent.)
Please don't post more of these without going back and indicating what YOU THINK about each one ... or what YOUR specific QUESTION is about each one.
I have been trying to figure out the problems I am posting but I don't understand how to solve them. I don't want just the answers I really want to understand how to solve them. I apologize for not asking a question I am not familiar with how this works. I was not dumping my homework.
OK ... but it will help our math tutors if you give them some idea of what you do and don't understand about each one.
I have tried to use what I thought was the right equations to solve the problems. But I am just absolutely lost when it comes to compound interest, solving for Annual Percentage Yield, and present value.
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To compute the amount of compound interest earned in 1 year, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after time t, including interest.
P is the principal amount (the initial investment).
r is the annual nominal interest rate (as a decimal).
n is the number of times that interest is compounded per year.
t is the number of years.
In this case, the principal amount is $1,000,000, the annual nominal interest rate is 8% (or 0.08 as a decimal), and interest is compounded quarterly, which means n = 4. Since we're calculating the interest earned in 1 year, t = 1.
Plug these values into the formula:
A = $1,000,000(1 + 0.08/4)^(4 * 1)
A = $1,000,000(1 + 0.02)^4
A = $1,000,000(1.02)^4
A ≈ $1,082,434.24
So, the amount of compound interest earned in 1 year is approximately $82,434.24.
To compute the Annual Percentage Yield (APY), we can use the formula:
APY = (1 + r/n)^n - 1
Where:
r is the annual nominal interest rate (as a decimal).
n is the number of times that interest is compounded per year.
In this case, r = 0.08 and n = 4 (compounded quarterly).
Plug these values into the formula:
APY = (1 + 0.08/4)^4 - 1
APY = (1 + 0.02)^4 - 1
APY = (1.02)^4 - 1
APY ≈ 0.0824 or 8.24%
Therefore, the Annual Percentage Yield (APY) for the investment is approximately 8.24%.