After graduating from MSU with a degree in Business, Jacob took a position at JP Morgan in Chicago. His goal is to set aside funds for the next 8 years to make down payment on a house. After consider- ing various suburbs in Chicagoland, Jacob decided on Naperville as his desired choice. The median home price in Naperville is $513,000. To avoid paying Private Mortgage Insurance, Jacob wanted to make a 20% down payment.

Historically median house prices in Naperville has increased by nearly 6% per annum, which he thinks is a reasonable estimate of the future.

JP Morgan provides several investment opportunities for its em- ployees and he decided to go with an investment opportunity that provides 10% return, given his risk preference.

1. Given his preference to buy a house in Naperville after 8 years, what amount should Jacob accumulate so that he can put a down of 20% on a reasonable house.

2. Base on your answer to 1, how much should he deposit in his investment account (that earns 10%) at the end of each month to accumulate the desired amount?

3. If Jacob decides to make end of the year deposit in the invest- ment instead of the monthly deposit. Will the yearly deposit be just equal to 12 times the monthly deposit. Why or Why not? What should the yearly deposit in the account be?

4. Due to economic condition house prices increased only by 3%, what would be his monthly payment in the investment account under the revised estimate?

5. Suppose there is a change in his risk perception and now he wants to go really safe with his investment. He now wants to invest in CDs of 3 major banks that offers only 4.5% return. How much should be his monthly deposits in CDs be to achieve his goal. Assume that growth on home prices in Naperville is still 3%.

please neatly type / write out equations used and the solutions