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
$4000*((1.0105)^(5*1)-1)/(0.0105) 20424.43

To get the future value of the annuity in 5 years, you can use the formula for the future value of an annuity:

FV = P * [(1+r)^n - 1] / r

Where:
FV = Future value of the annuity
P = Payment per period ($4000 in this case)
r = Interest rate per period (10.5% or 0.105)
n = Number of periods (5 years)

Plugging in the values into the formula:

FV = $4000 * [(1+0.105)^(5*1) - 1] / 0.105
FV = $4000 * [(1.0105)^(5) - 1] / 0.105
FV = $4000 * [(1.0105)^(5) - 1] / 0.105
FV = $4000 * [1.051030125 - 1] / 0.105
FV = $4000 * 0.051030125 / 0.105
FV = $20412.12

So, the future value of the annuity in 5 years would be approximately $20412.12.

To calculate 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 (4 years), you can subtract the future value of the annuity from the future value of the regular compounded interest account.

Assuming the regular compounded interest account has the same interest rate of 10.5% and compounds annually, you can calculate the future value using the formula:

FV = P * (1 + r)^n

Where:
FV = Future value
P = Principal amount ($4000 * 5 = $20,000 in this case, as it's the total amount paid over the 5 years)
r = Interest rate per period (10.5% or 0.105)
n = Number of periods (4 years, as stated in the question)

Plugging in the values into the formula:

FV = $20000 * (1 + 0.105)^4
FV = $20000 * (1.105)^4
FV = $20000 * 1.48522
FV = $29704.40

So, the future value of the regular compounded interest account with the same term would be approximately $29704.40.

To find how much more interest would be earned, we subtract the future value of the annuity ($20412.12) from the future value of the regular compounded interest account ($29704.40):

$29704.40 - $20412.12 = $9292.28

Therefore, the owner would earn approximately $9292.28 more interest if they could invest the full amount paid into the annuity in a regular compounded interest account with the same term.

A. The future value of the annuity in 5 years is approximately $20,424.43.

B. To calculate the interest earned in a regular compounded interest account with the same term (4 years) and an annual interest rate of 10.5%, we can use the formula:

Interest earned = Principal * ((1 + interest rate)^time) - Principal

In this case, the principal is $4000 and the time is 4 years. Plugging in these values, we get:

Interest earned = $4000 * ((1 + 0.105)^4) - $4000

Interest earned = $4000 * ((1.105)^4) - $4000

Interest earned = $4000 * (1.4642386) - $4000

Interest earned = $5856.95 - $4000

Interest earned = $1856.95

Therefore, the owner would earn approximately $1856.95 more in interest if they could invest the full amount paid into the annuity in a regular compounded interest account with the same term.