Answer:
Percentage of the first 25 payments goes toward paying principal is 41.95%.
Explanation:
Note: See the attached excel file for the amortization schedule for the first 25 months.
In the attached excel file, the monthly is calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value or the balance to pay = Cost * (100% - Percentage of down payment) = $100,000 * (100% - 10%) = $90,000
P = Monthly payment = ?
r = Monthly interest rate = Nominal rate / 12 = 3% / 12 = 0.25%, or 0.0025
n = number of months to repay = 30 years * 12 months = 360
Substitute the values into equation (1) and solve for P, we have:
$90,000 = P * ((1 - (1 / (1 + 0.0025))^360) / 0.0025)
$90,000 = P * 237.189381504283
P = $90,000 / 237.189381504283
P = $379.44
From the attached excel file, we have:
Total payment for the first 25 months = $9,486.09
Total repayment of principal for the first 25 months = $3,979.17
Therefore, we have:
Percentage of the first 25 payments goes toward paying principal = (Total repayment of principal for the first 25 months / Total payment for the first 25 months) * 100 = ($3,979.17 / $9,486.09) * 100 = 41.95%
