Question

the loan is$ 50,000 at 9%for 7 years ? what is the first payment and the unpaid balance after the first year

Answer 1

Is this simple interest or compounded?

If compounded, how?
Yearly, quarterly, annually ?

Answer 2

Loan is $50,000 at 9% for 7 years.

Calculate Monthly Payment
P = iA/(1 - (1 + i)^-N
P = payment amount (per month)
i = Interest Rate = 0.09/12 = 0.0075
A = Loan amount = 50,000
N = number of payments = 84

P = 0.0075(50,000)/(1 - (1+0.0075)^-84)
P = 375/(1 - (1.0075)^-84)
P = 375/(1 - 0.533845)
P = 375/0.466155
Payment = $804.45

Calculate Balance After 1 year
B = A(1 + i)^n - P/i ((1+i)^n - 1)
A = Loan amount = 50,000
i = Interest Rate = 0.09/12 = 0.0075
n = number of payments = 12
P = Payment amount = 804.45

B = 50000(1+0.0075)^12 - 804.45/0.0075 *
((1+0.0075)^12 - 1)

B = 50000(1.0075)^12 - 107260 * ((1.0075)^12 - 1)

B = 50000(1.09381) - 107260 * (1.09381 - 1)

B = 54690.50 - 107260(0.09381)
B = 54690.50 - 10062.06
Balance = 44,628.44