Question

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.

Answer 1

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

Answer 2

Thanks for the explanation Henry!