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.
1.05^2 - 1 = 10.25 APY Wilder
1.0081666^12 - 1 = 10.2524 APY Cheapskate
so go with cheapskate
ten years
1.05^20 =2.6532
*85,000 = 225,530.30
1.0008166667^120 = 2.65387
*85,000 = 225,579.18
Cheapskate is 48.88 better
To compare the two investment options, let's calculate the Annual Percentage Yield (APY) for each option.
a) APY Calculation:
For Wilder Revenue:
1. Convert the annual interest rate to a semiannual rate: 10% divided by 2 = 5%.
2. Calculate the APY using the semiannual rate: APY = (1 + 5%)^2 - 1.
For Cheapskate Investments:
1. Convert the annual interest rate to a monthly rate: 9.8% divided by 12 = 0.8167%.
2. Calculate the APY using the monthly rate: APY = (1 + 0.8167%)^12 - 1.
Now, let's determine which investment option has a higher APY to choose where Jason should invest.
b) Future Value Calculation:
To calculate the future values of the investments over ten years, we can use the Compound Interest Formula:
Future Value (FV) = P * (1 + r/n)^(n*t)
Where:
P = Principal (the initial investment)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Time period in years
For Wilder Revenue:
FV = $85,000 * (1 + 5%/2)^(2*10)
For Cheapskate Investments:
FV = $85,000 * (1 + 0.8167%/12)^(12*10)
Now, let's calculate the future values for both options and determine how much more they will earn with the chosen option from part a.
By comparing the APYs and calculating the future values, we can determine where Jason should invest and how much more they will earn.