What is the monthly payment for a 10-year, $24,000 loan at 4.625% APR

I have no idea how to calculate APR or monthly payments :)

Also what would the total interest that's paid on the loan?

Does anybody know of a website that has a calculator for this kind of thing?

I'll show you how to calculate monthly payments.

Let's suppose you had a loan that you needed to repay in 3 payments, and you were charged "i" annual interest

L = loan amount
i = interest rate
P = monthly payment

(((L * (1 + i/12) - P) * (1 + i/12) - P) * (1 + i/12) - P = 0

Let 1 + i/12 = r

(((L * r - P) * r - P) * r - P = 0

Solve for L

((Lr - P) * r - P = P/r
Lr - P = P/r + P/r^2
L = P/r + P/r^2 + P/r^3
L = P * ((1/r) + (1/r)^2 + (1/r)^3)

Now, if you've ever learned about geometric sums, you'd recognize (1/r) + (1/r)^2 + (1/r)^3 as a sum. Now, before I solve that sum (make it easier to manage), let's suppose that we had a different number of payments. We'll call that number "n"

L = P * ((1/r) + (1/r)^2 + (1/r)^3 + ... + (1/r)^n)

Can we make it easier to manage? Absolutely!

Let (1/r) = t, and let (1/r) + (1/r)^2 + ... + (1/r)^n sum to S

S = (1/r) + (1/r)^2 + ... + (1/r)^n
S = t + t^2 + t^3 + ... + t^n

Multiply both sides by t and solve for S

S * t = t * (t + t^2 + t^3 + ... + t^n)
S * t = t^2 + t^3 + t^4 + ... + t^(n + 1)

S - St = t + t^2 - t^2 + t^3 - t^3 + .... + t^n - t^n - t^(n + 1)

Notice most terms cancel out on the right hand side

S - St = t - t^(n + 1)
S - St = t * (1 - t^n)
S * (1 - t) = t * (1 - t^n)
S = t * (1 - t^n) / (1 - t)

So:

t + t^2 + t^3 + .... + t^n = t * (1 - t^n) / (1 - t)


L = P * S
L = P * t * (1 - t^n) / (1 - t)
P = L * (1 - t) / (t * (1 - t^n))

t = 1/r
r = 1 + i/12


First, let's calculate monthly payments

L = 24000
n = 10 * 12 = 120 payments