Question 2 requires the more complex answer because the number of days in each month varies, although it can be calculated using a spreadsheet. Some of the other parts can be answered using formulae which I have attempted to do.
You have not stated your simple interest model so some suppositions are made in the answer to question 1. Comments welcome.
Start Principal = $21,315.00
Date of Disbursement = 9/16/19
APR = 3.99%
Payment monthly: $333.41 on Day 16 of month
Compound Period = Daily (360 days/yr)
Using the following variables
s = principal
r = periodic rate
n = number of periods
d = periodic payment
Standard loan equation
d = r s (1/((1 + r)^n - 1) + 1) Formula 1
s = 21315
r = 3.99/100 * 30/360
d = 333.41
∴ n = -(log(1 - (r s)/d)/log(r + 1)) = 71.9927
You could round this to 72 months, in which case the term is 6 years.
total interest = 72 d - s = 2690.52
Simple interest over 6 years would result in
total interest = s * 3.99/100 * 6 = 5102.81
However, if the term is unknown for the simple interest application it can be calculated since the interest plus principal should equal the sum of the payments
s r n + s = n d
∴ n = s/(d - r s) = 81.1884 months
∴ total simple interest = 81.1884 d - s = 5754.02 approximately
Some rather high figures using simple interest.
PV = $15,020.00
PV Date = 10/8/19
APR = 3.99%
Payment = $208.25 per month on day 12 of month
Compound Period = Monthly
Find the balance on the 12th, after 4 days' interest.
s = 15020
r = 3.99/100/12
dailyrate = (1 + r)^(12/365) - 1 = 0.00010914
s = s (1 + dailyrate)^4 = 15026.56
Step back one month to use the regular formulae (with payment at month-end)
s = s/(1 + r) = 14970.22
∴ n = -(log(1 - (r s)/d)/log(r + 1)) = 82.2865 months
Using formula 2 to find the balance after 82 months
x = 82
∴ b = (d + (1 + r)^x (r s - d))/r = 59.5334
total interest = 82 d + b (1 + r) - 15020 = 2116.23
I don't have time to check out a simple interest calculation for question 3, so I'm posting the calculations as they are. Hopefully they're of some help or serve as a conversation starter.
- Formula for periodic payment - loan payment formula
- Formula for loan balance - inhomogeneous difference equation (Arne Jensen, Aalborg Uni.)