Answer: $23,653.18
Explanation:
Let
[tex]P = \text{Principal loan amount} = \$660,000
\\ \indent r = \text{annual percentage rate} = 8.35 \% = 0.0835 \\ \indent N = \text{number of annual payments} = 15
[/tex]
Then, we can use the mortgage formula because we can treat N as the number of payments and the rate that we'll be using in the formula is the apr = 8.35%.
So, the annual payment is calculated as: (Note: change 8.35% to decimal)
[tex]A = \frac{rP}{1 - (1 + r)^{-N}}
\\
\\ \indent A = \frac{(0.0835)(660,000)}{1 - (1 + 0.0835)^{-15}}
\\
\\ \indent A = \frac{55,110}{1 - (1.0835)^{-15}}
\\
\\ \indent \boxed{A = \$78,763.18}
[/tex]
Now, we need to calculate the interest amount in the first year, which is given by
Interest Amount = rP
= (0.0835)(660,000)
Interest Amount = $55,110
Now, we let [tex]p_1[/tex] be the amount to be reduced from the principal balance. Then,
[tex]p_1 = \text{(annual payment) - (interest amount)}
\\\indent p_1 = \$78,763.18 - \$55,110.00
\\\indent \boxed{p_1 = \$23,653.18}
[/tex]
Hence, $23,653.18 will be used to reduce the prinicipal balance.
