Question: When applying for a mortgage, you should find one that allows you to be able to pay more money than the required monthly payment. The following problem illustrates why. Let's say that you have a 30-year $150,000 fixed-rate mortgage at 4% interest compounded monthly. Instead of paying the regular monthly payment for the mortgage, you decide to add an additional $100 to each of your monthly payments. By paying the extra $100 a month, the extra amount in each payment is applied directly to reducing the principal. This means that (1) the length of the loan is reduced since the principal will be reduced faster (than if no extra amount was paid with your monthly payment) and (2) you eventually pay less in interest than if you were to pay just the required monthly payment. Answer the following:
A. How many years will it take you to pay off the loan if you were to pay the additional $100 with each monthly payment? Use the TVM Solver. Show how you arrived at your answer.
B. How much money will you save in interest if you pay the additional $100 with each monthly payment by comparison with not paying an additional amount each month? Show how you arrived at your answer and round it to the nearest dollar.
A newly married couple decides to keep having children until they have a boy. What is the probability that the couple will have at least three children? Assume there are no multiple births and the probability of having a boy is the same as having a girl. Show all the work needed to solve this problem.
A husband, a wife, and their six children randomly stand in a row for a family picture. What is the probability that the parents will be standing next to each other? Show how you arrived at your answer.