Jason Printing has $85,000 to invest. They can invest in Wilder Revenue at 10% compounded semiannually or at Cheapskate Investments at 9.8% compounded monthly.
a. Calculate the two APYs and compare them to determine your answer. Make sure to distinguish which APY belongs to which banks. At which bank should they invest?
b. If they were to invest this money for ten years. How much more money will they earn if investing with your choice from part a? Compare the two future values.
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a. To compare the two investment options, we need to calculate the Annual Percentage Yield (APY) for each bank.
1. Wilder Revenue at 10% compounded semiannually:
The formula to calculate APY is: (1 + (r/n)) ^ n - 1, where r is the interest rate and n is the number of compounding periods in a year.
For Wilder Revenue, the interest rate is 10% and it is compounded semiannually, so n = 2.
APY for Wilder Revenue = (1 + (0.1/2))^2 - 1
2. Cheapskate Investments at 9.8% compounded monthly:
Again, using the formula for APY:
For Cheapskate Investments, the interest rate is 9.8% and it is compounded monthly, so n = 12.
APY for Cheapskate Investments = (1 + (0.098/12))^12 - 1
Now that we have the APY for both banks, we can compare them to determine which bank gives a higher return.
b. To calculate the future value, we can use the formula: FV = P*(1 + r/n)^(n*t), where FV is the future value, P is the principal (initial investment), r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
Using this formula, we can calculate the future value for each bank and compare the difference.
Let's plug in the numbers and calculate the APYs and future values for both banks:
1. Wilder Revenue:
APY for Wilder Revenue = (1 + (0.1/2))^2 - 1
Future Value (FV) = $85,000 * (1 + (0.1/2))^(2*10)
2. Cheapskate Investments:
APY for Cheapskate Investments = (1 + (0.098/12))^12 - 1
Future Value (FV) = $85,000 * (1 + (0.098/12))^(12*10)
Calculate the APYs and future values for both banks using the formulas above. Compare the APYs to determine which option provides a higher return. To determine the difference in earnings over ten years, subtract the future value of one bank from the future value of the other bank. The bank with the higher future value will result in more earnings over the ten-year period.