Questions Regarding Time Value of Money ( Please use 2 decimal points for your calculation. )

1. You plan to accumulate $450,000 over a period of 12 years by making equal annual deposits in an account that pays an annual interest rate of 9% (assume all payments will occur at the beginning of each year). What amount must you deposit each year to reach your goal?

2. You are planning to buy your dream mansion and for that you have decided to make 3 independent investments with your savings money in the next 44 years. You plan to invest $4,100 at the end of each year for the first 17years, $6,900 at the end of each year for the following 11 years, $14,500 at the end of each year for the last 16 years. You believe you will earn an effective annual rate of return of 9.7% on your investment. If the price of your dream mansion will be $1,000,000 after 44 years, will you be able to fulfill your dream with those 3 investments?

3. You can invest $77000 today with an annual interest rate of 12% for 40 years. If you decide to deposit the same amount after 14 years, instead of today, how better or worse off would you be? In reality, you dont have enough money to invest now. However, in 10 years you will have enough savings to invest. How much would you have to invest after 10 years from today with the same interest rate (12% EAR) to have the originally planned amount (FV of investing $77000 today for 40 years) after 40 years?