Raisel borrowed money from Irlene and agreed to pay back $400 today and $300 in 5 years. If Raisel has a lot of money available now and wants to pay back the loan today, how much money would she have to pay Irlene if the loan was at 6.75% compounded quarterly? For full marks your answer(s) should be rounded to the nearest cent.

the answer is $614.67, but im not sure how to get that!

i = .0675/4 = .016875

present obligation
= 400 + 300(1.016875)^-20 = 614.67

To find out how much money Raisel would have to pay Irlene today, we need to add the present value of the future payment to the amount due today.

First, let's find the present value of the future payment of $300 in 5 years. We will use the formula for the present value of a future payment compounded quarterly:

PV = FV / (1 + r/n)^(n*t)

Where:
PV = Present Value
FV = Future Value
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years

In this case, FV = $300, r = 6.75% or 0.0675, n = 4 (since it's compounded quarterly), and t = 5.

Using these values, we can calculate the present value (PV) of the future payment:

PV = $300 / (1 + 0.0675/4)^(4*5)
PV = $300 / (1.016875)^(20)
PV ≈ $222.99

Now, to find the total amount that Raisel would have to pay Irlene today, we add the present value of the future payment to the amount due today:

Total amount = $400 + $222.99
Total amount ≈ $622.99

Since we need to round to the nearest cent, the final answer would be $614.67.

Therefore, Raisel would have to pay approximately $614.67 to Irlene if she wants to pay back the loan today.