The owner of Campus Cafe plans to open a second location on a satellite campus in 5yrs. She buys an annuity that pays 10.5% interest compounded annually
A. If the payment is $4000 a year, find the future value of the annuity in 5yrs.
B. How much more interest would be earned if the owner could invest the full amount paid into the annuity in a regular compounded interest account with the same term for 4 years .
Can someone please help me thank you
Sure, I can help you with that!
To find the future value of an annuity, you can use the formula for the future value of an ordinary annuity:
Future Value = Payment × [(1 + Interest Rate)^(Number of Periods) - 1] / Interest Rate
Let's calculate the future value of the annuity first:
A. Future Value = $4000 × [(1 + 0.105)^(5) - 1] / 0.105
= $4000 × [(1.105)^5 - 1] / 0.105
Now, to calculate the future value, we just need to substitute the values into the formula and solve the equation.
Let's calculate the future value using a calculator or a spreadsheet software:
Future Value = $4000 × [(1.105)^5 - 1] / 0.105
≈ $4000 × (1.64701 - 1) / 0.105
≈ $4000 × 0.64701 / 0.105
≈ $24,812.86
So the future value of the annuity after 5 years would be approximately $24,812.86.
Now moving onto the second part of the question:
B. To calculate the additional interest that could be earned if the full amount paid into the annuity were invested in a regular compounded interest account, we need to calculate the future value of that investment using the same term of 4 years.
The formula for calculating future value with compound interest is:
Future Value = Principal × (1 + Interest Rate)^(Number of Periods)
Let's calculate the future value of the investment:
Principal = $4000 × 4 = $16,000 (total amount paid into the annuity over 4 years)
Interest Rate = 10.5% = 0.105
Number of Periods = 4
Future Value = $16,000 × (1 + 0.105)^4
≈ $16,000 × (1.105)^4
≈ $16,000 × 1.48685
≈ $23,789.60
Now, to calculate the additional interest earned, we subtract the future value of the annuity from the future value of the investment:
Additional Interest = Future Value of Investment - Future Value of Annuity
= $23,789.60 - $24,812.86
≈ -$1,023.26
Therefore, if the owner could invest the full amount paid into the annuity in a regular compounded interest account, they would earn approximately -$1,023.26 less in interest compared to the annuity.
Note: It is important to double-check the calculations and ensure the interest rate and time periods are accurate for your specific scenario.