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# Time value of money

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1. Housing rates have rapidly increased, and you have decided to save to buy your first house. You expect to save \$1500 per month at the end of each month for the next 3 years, investing these funds in a mutual fund you expect to earn 6.5% interest, compounded monthly. At the end of three years of savings, you will buy the house with your savings, and use the \$1500 per month as your mortgage payments. If interest rates on mortgages are 7% compounded monthly in three years, and you will take a 30-year mortgage, paying at the beginning of each month.
a. How much of a mortgage can you obtain given the above information?
b. How much of a down payment will you have saved to buy your house in 3 years?
c. What is the total value of the house you will be able to purchase given this information?
2. A friend of yours just won the lottery. She has been given the choice of \$5,000,000 today, or \$700,000 per year for the next 10 years, at the beginning of each year.. If she received the \$5 million immediately, she would invest in a balanced asset fund she expects to earn 8%, compounded annually. Which option should she take?
3. You are saving for retirement with a \$4,000 investment in a traditional IRA at the end of each year, and are investing the funds into a mutual fund you expect to earn 7.75% interest, compounded quarterly.
a. How much will you have saved towards retirements in 35 years if you make your investment on Jan. 1 each year?
b. How much will you have saved towards retirement in 35 years if you make your investment on December 31 each year?
4. You have decided to start investing in the stock market, and buy a small cap mutual fund with a price of \$31. The fund's value has been growing at 14% per year.
a. How many years will it take the fund's price to triple in price at this growth rate?
b. If you hold the fund for 6 years, then sell it at \$72, compute the growth rate for each year.
5. You have a credit card offer. It carries an 18% interest rate, compounds monthly, and you will transfer \$2,000 to the card. If you pay the minimum payment of 2% of the balance, or \$40 at the end of each month, how many years will it be before you pay off the balance completely? To solve this algebraically, you have to manipulate the equation to isolate the unknown variable, then use natural logs to solve.