It is Jan 1 2010. Celeste Cheung and her husband are considering buying their first home. The cost of the house now is $320,000. They have two options. Option A: Buy the house now and apply for a $320,000, 30-year mortgage. Under the terms of the mortgage, they will receive $320,000 today to help purchase their home. The loan will be fully amortized over the next 30 years. Current mortgage rates are 9%. Interest is compounded monthly and all payments are due at the end of the month. Option B: Delay buying the house for ten years and live with Celeste’s parents. During these ten years, Celeste and her husband hope to save enough money to pay off the full amount of the house in cash without taking out a loan. They plan to save a fixed amount of money every month in a brokerage account that yields a nominal annual interest rate of 12% with monthly compounding. The deposits will be made at the beginning of each month, with the first deposit being made today and the last deposit will be made on 1 December 2019. They will use their savings to pay for the house on 31 December 2019. They estimate that house price will increase at the overall inflation rate. Inflation is expected to average 4% for the next 10 years.

 

(a) If Celeste chooses Option A, what will be the monthly mortgage payment?

(b) What will be the remaining balance on the mortgage after the 24^th payment?

(c) If Celeste chooses Option B, how much will she have to deposit in the brokerage account every month?