A individual is borrowing 195,000 for a 15 year loan at 3.57% per year compounded monthly. Calculate her monthly payment

Accepted Solution

Answer:Her monthly payment is $1849.19Step-by-step explanation:To find how much she has to pay monthly, firstly we have to see how much she is going to owe in 15 years, then we divide that by 180(each has has 12 months, 15 years * 12 months = 180 months).We can find how much she owns by the compound interest formula, that is given by:[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.In this exercise, we have:A is the value we want to findP = 195,000r = 0.0357n = 12, since the interest is compounded monthly, and there are 12 months in a year.t = 15.The amount is:[tex]A = P(1 + \frac{r}{n})^{nt}[/tex][tex]A = 195,000(1 + \frac{0.0357}{12})^{12*15}[/tex][tex]A = 332,854.20[/tex]She has to pay $332,854.20 in 180 months. So, her monthly payment is[tex]M = \frac{332,854.20}{180} = 1849.19[/tex]