For a $13,000 student loan with a 6% APR, how much of the payment will go toward the principal and how much will go toward paying interest for each of the first six payments? Assume this is a 10-year loan with monthly payments.
P = Po*r*t/(1-(1+r)^-t)
Po = $13,000 = Loan amount.
r = (6%/12)/100% = 0.005 = Monthly %
rate expressed as a decimal.
t = 12mo/yr * 10yrs = 120 Months.
P = (13000*0.005*120)/(1-(1.005)^-120) =
$17,319.20 = Amt. to be paid.
Monthly Payment = P/t = 17319.20/120 =
$144.33
Payment Interest Principal Balance
0.00 0.00 0.00 13,000.00
144.33 65.00 79.33 12,920.67
144.33 64.60 79.73 12,840.94
144.33 64.20 80.13 12,760.82
144.33 63.80 80.53 12,680.29
144.33 63.40 80.93 12,599.35
144.33 63.00 81.33 12,518.03
Calculations:
1. Int. = P*r*t = 13000*0.005*1yr=65.00
2. Int.=p*r*t = 12,920.67*0.005*1=64.60
3. Int.=P*r*t = 12,840.94*0.005*1=64.20
Thanks for the explanation Henry!
To determine how much of each payment goes toward the principal and the interest, we need to use an amortization schedule. This schedule breaks down each payment and shows how much is allocated toward interest and principal.
To calculate the monthly payment, we can use the formula for calculating a fixed monthly payment on a loan:
PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT = monthly payment
P = principal loan amount
r = monthly interest rate
n = total number of payments
Let's calculate the monthly payment first:
P = $13,000
APR = 6%
Monthly interest rate (r) = 6% / 12 = 0.005
Now, we need to calculate the total number of payments (n). Since it is a 10-year loan with monthly payments, the total number of payments will be 10 * 12 = 120.
Using the formula, we can calculate the monthly payment:
PMT = (13000 * 0.005 * (1 + 0.005)^120) / ((1 + 0.005)^120 - 1)
≈ $145.80 (rounded to the nearest cent)
Now that we have the monthly payment amount, we can calculate how much goes towards the principal and interest for each of the first six payments.
To do this, we'll use the amortization formula:
Principal Payment = Monthly Payment - Interest Payment
Interest Payment = Previous Remaining Balance * Monthly Interest Rate
Remaining Balance = Principal - Sum of Previous Principal Payments
Let's calculate the principal and interest distribution for the first six payments:
Payment 1:
Interest Payment = $13,000 * 0.005 = $65.00
Principal Payment = $145.80 - $65.00 = $80.80
Payment 2:
Interest Payment = ($13,000 - $80.80) * 0.005 = $64.60
Principal Payment = $145.80 - $64.60 = $81.20
Payment 3:
Interest Payment = ($13,000 - $80.80 - $81.20) * 0.005 = $64.30
Principal Payment = $145.80 - $64.30 = $81.50
Payment 4:
Interest Payment = ($13,000 - $80.80 - $81.20 - $81.50) * 0.005 = $63.99
Principal Payment = $145.80 - $63.99 = $81.81
Payment 5:
Interest Payment = ($13,000 - $80.80 - $81.20 - $81.50 - $81.81) * 0.005 = $63.69
Principal Payment = $145.80 - $63.69 = $82.11
Payment 6:
Interest Payment = ($13,000 - $80.80 - $81.20 - $81.50 - $81.81 - $82.11) * 0.005 = $63.39
Principal Payment = $145.80 - $63.39 = $82.41
So, for the first six payments, the breakdown of principal and interest payments would be as follows:
Payment 1: Principal Payment = $80.80, Interest Payment = $65.00
Payment 2: Principal Payment = $81.20, Interest Payment = $64.60
Payment 3: Principal Payment = $81.50, Interest Payment = $64.30
Payment 4: Principal Payment = $81.81, Interest Payment = $63.99
Payment 5: Principal Payment = $82.11, Interest Payment = $63.69
Payment 6: Principal Payment = $82.41, Interest Payment = $63.39