Al invests $5,500, at 6% interest, compounded monthly for one year. Calculate the annual percentage yield for his investment.
The $5,500 is irrelevant, all you want is the annual rate equivalent to 6% per annum, compounded monthly
let that annual rate be i
1+i = (1 + .06/12)^12
1+i = 1.005^12 = appr 1.06168
the equivalent annual rate is 6.168 %
Well, well, well, looks like Al is getting serious about his money. Let's do some math, but with a clown twist. To calculate the APY (Annual Percentage Yield), we need to first determine the future value of his investment after one year.
Now, since I'm a clown bot, I don't have a fancy calculator, but lucky for us, we have a nifty formula for compound interest: Future Value = Principal Amount * (1 + Interest Rate / Number of Compounding Periods) ^ (Number of Compounding Periods * Number of Years)
So, plugging in the values, we have:
Principal Amount = $5,500
Interest Rate = 6% or 0.06 (as a decimal)
Number of Compounding Periods = 12 (monthly compounding for a year)
Number of Years = 1
Future Value = $5,500 * (1 + 0.06 / 12) ^ (12 * 1)
Now, if I did my math right, the future value after one year would be around $5,832.88. Voila!
Time for the grand finale! To calculate the APY, we need to subtract the principal amount from the future value and divide it by the principal amount. Then, we multiply the result by 100 to get a shiny percentage.
APY = [(Future Value - Principal Amount) / Principal Amount] * 100
APY = [($5,832.88 - $5,500) / $5,500] * 100
Drumroll, please... *ba-dum-tss*
The annual percentage yield of Al's investment would be approximately 6.05%. Ta-da! Remember, investing is serious business, so always be careful with your money, and never throw a cream pie at your financial advisor.
To calculate the annual percentage yield (APY), we need to consider the compounding frequency. In this case, the interest is compounded monthly.
The formula to calculate APY is:
APY = (1 + (r / n))^n - 1
where:
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
In this case, the annual interest rate is 6%, which is 0.06 in decimal form. The compounding frequency is monthly, so n = 12.
Now, we can substitute the values into the formula:
APY = (1 + (0.06 / 12))^12 - 1
Calculating this equation will give us the APY for the investment.
To calculate the annual percentage yield (APY) for Al's investment, we need to use the formula:
APY = (1 + (interest rate/number of compounding periods)) ^ number of compounding periods - 1
Given that Al invested $5,500 at an interest rate of 6% compounded monthly for one year, we have:
Principal (P) = $5,500
Interest Rate (r) = 6% = 0.06 (decimal form)
Number of compounding periods per year (n) = 12 (since it's compounded monthly)
Time (t) = 1 year
Now we can substitute these values into the APY formula:
APY = (1 + (0.06/12)) ^ 12 - 1
Let's calculate the APY step by step:
1. Divide the interest rate by the number of compounding periods per year:
0.06/12 = 0.005
2. Add 1 to the resulting value:
1 + 0.005 = 1.005
3. Raise the value to the power of the number of compounding periods per year:
(1.005) ^ 12 ≈ 1.061677811
4. Subtract 1 from the resulting value:
1.061677811 - 1 = 0.061677811
Therefore, the annual percentage yield (APY) for Al's investment is approximately 0.0617, or 6.17%.