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 bank. At which bank should they invest?
b) If they were to invest this money for ten years. How much more will they earn if investing with your choice from part a? Compare the two future values.
Wilder:
amount = 85000(1.05)^2 = $93,712.50 after 1st year
Cheapskate:
amount = 85000(1.0081666..)^12 = $93,714.53 after 1st year
b) you try it, (you only have to change the exponents)
a) To calculate the APY (Annual Percentage Yield) for each investment, we need to use the formula:
APY = (1 + (interest rate / number of compounding periods))^number of compounding periods - 1
1. Wilder Revenue:
Interest Rate: 10% compounded semiannually
Number of Compounding Periods: 2 (since it is compounded semiannually)
APY = (1 + (0.10 / 2))^2 - 1
APY = (1 + 0.05)^2 - 1
APY = 1.1025 - 1
APY = 0.1025 or 10.25%
2. Cheapskate Investments:
Interest Rate: 9.8% compounded monthly
Number of Compounding Periods: 12 (since it is compounded monthly)
APY = (1 + (0.098 / 12))^12 - 1
APY = (1 + 0.0081667)^12 - 1
APY = 1.1024 - 1
APY = 0.1024 or 10.24%
Comparing the two APYs:
- Wilder Revenue has an APY of 10.25%
- Cheapskate Investments has an APY of 10.24%
Therefore, based on the APY, Jason Printing should invest at Wilder Revenue since it offers a slightly higher return.
b) To calculate the future value of an investment over ten years, we can use the formula:
Future Value = Principal * (1 + interest rate / number of compounding periods)^(number of compounding periods * number of years)
Let's calculate the future value for each investment and compare them:
1. Wilder Revenue:
Principal: $85,000
Interest Rate: 10% compounded semiannually
Number of Compounding Periods: 2 (since it is compounded semiannually)
Number of Years: 10
Future Value = $85,000 * (1 + (0.10 / 2))^(2 * 10)
Future Value = $85,000 * (1 + 0.05)^20
Future Value = $85,000 * (1.05)^20
Future Value = $85,000 * 2.65329770577
Future Value β $225,535.08
2. Cheapskate Investments:
Principal: $85,000
Interest Rate: 9.8% compounded monthly
Number of Compounding Periods: 12 (since it is compounded monthly)
Number of Years: 10
Future Value = $85,000 * (1 + (0.098 / 12))^(12 * 10)
Future Value = $85,000 * (1 + 0.0081667)^120
Future Value = $85,000 * (1.0081667)^120
Future Value = $85,000 * 2.59254812271
Future Value β $220,163.89
Comparing the two future values:
- Investing with Wilder Revenue will earn approximately $225,535.08.
- Investing with Cheapskate Investments will earn approximately $220,163.89.
Therefore, by choosing Wilder Revenue from part a, Jason Printing will earn approximately $5,371.19 more over ten years compared to Cheapskate Investments.