the loan is$ 50,000 at 9%for 7 years ? what is the first payment and the unpaid balance after the first year
Is this simple interest or compounded?
If compounded, how?
Yearly, quarterly, annually ?
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
To calculate the first payment and the unpaid balance after the first year for a loan, you would need to know the loan term, interest rate, and the loan amount.
Given:
Loan amount = $50,000
Interest rate = 9%
Loan term = 7 years
First, to calculate the first payment, you can use the formula for calculating a loan payment known as the amortization formula:
Payment = (P * r * (1+r)^n) / ((1+r)^n - 1)
Where:
P = Principal loan amount
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments (loan term multiplied by 12)
1. Calculate the monthly interest rate:
r = (9% / 100) / 12 = 0.0075
2. Calculate the total number of monthly payments:
n = 7 years * 12 months/year = 84
3. Plug the values into the formula to find the first payment:
Payment = ($50,000 * 0.0075 * (1+0.0075)^84) / ((1+0.0075)^84 - 1)
Payment ≈ $735.73
So, the first payment on the loan would be approximately $735.73.
To calculate the unpaid balance after the first year, you need to determine how many payments have been made and subtract them from the total number of payments. In this case, since we are looking for the unpaid balance after the first year, that would be 12 monthly payments:
Total number of payments = 84
Number of payments made = 12
Number of payments remaining = 84 - 12 = 72
To calculate the unpaid balance, you can use the amortization formula again, but instead of finding the payment, you plug in the remaining number of payments into the formula:
Unpaid Balance = (P * (1+r)^n) - (((1+r)^n - 1) / r) * Payment
Unpaid Balance = ($50,000 * (1+0.0075)^72) - (((1+0.0075)^72 - 1) / 0.0075) * $735.73
Unpaid Balance ≈ $41,622.91
So, the unpaid balance after the first year would be approximately $41,622.91.