number of months = 3 years * 12 months per year = 36 months.
percent interest rate per month= 7.6 / 12 = .633333333 percent.
use the following online financial calculator.
https://arachnoid.com/finance/
to find the present value of the loan (the loan amount), do the following:
set present value = 0
set value = 0
set number of time periods = 3 years * 12 = 36 months.
set payment per month equal to -319.05
set percent interest rate per month = 7.6% / 12 = .63333333%.
set payments to be made at the end of each month.
click on pv and the calculator tells you that the present value of the loan is equal to $10,241.66.
that's the loan amount.
to find the future value of the loan, make the same inputs as for present value of the loan except click on fv rather than pv.
the calculator tells you that the future value of the loan is equal to $12,855.16.
the present+ value of the loan is how much you received from the bank.
the future value of the loan is how much the bank made from your payments.
the interest you paid on the loan is the sum of the payments minus the loan amount.
that would be 319.05 * 36 - 10241.66 = 1244.14.
the interest the bank made on the loan payments you gave them is the future value of the loan minus the sum of the payments = 12855.16 - 319.05 * 36 = 1369.36.
the money they lent you is equivalent to them investing that money at 7.6% per year compounded monthly for 36 months.
the formula for that is f = p * (1 + r) ^ n
f is the future value.
p is the present value - 10241.66
r is the interest rate per time period = .076/12
n is the number of time periods = 3 * 12 = 36
the formula becomes f = 10241.66 * (1 + .076/12) ^ 36 = 12855.16 rounded to the penny.
in the calculator, you make the payments negative because it's money going out.
the present value and the future value are then positive because it's money coming in.
the present value is money coming in to you.
the future value is the money coming in to the bank.
if you had made the payments positive, the present value and the future value would have then shown as negative.
it's a calculator and cash flow convention.
here's what the calculator inputs and outputs look like.
+