### Finance problems involving the time value of money

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Good day, looking for assistance in obtaining the proper solutions to these finance problems involving the time value of money.

1. You annually invest \$1,500.00 in an IRA starting at age 20 and make the contributions for 10 years. your twin sister does the same starting at age 30 and makes contributions for 30 years.  Both of you earn 7 percent annually on your investment.  Wo has the larger amount at age 60?

2. you are offered an annuity that will pay \$10,000 a year for 10 years (that is 10 payments) starting after five years has elapsed.  if you seek an annual return of 8 percent what is the maximum amount you should pay for this annuity?

3. you wish to retire in 12 years and currently have \$50,000 in a savings account yielding 5 percent annually, \$100,000 in quality "blue chip" stocks yielding 10 percent.  If you expect to add \$30,000 at the end of each year to your stock portfolios how much will you have in your retirement fund when you retire?  What rate of return must you earn on you retirement funds if you want to withdraw \$102,000 per year for the next 15 years after retiring?

4. A savings and loan association finances your 25-year, \$100,000, 9 percent mortgage.  How much interest does the S&L collect on the loan in the second year.

5.  You contribute \$1000 annually to a retirement account for 8 years and stop making payments at the age of 25.  Your twin brother opens an account at age 25 and contributes \$1000 a year until retirement at age 65 (40 years).  You both earn 10 percent on your investments.  How much can each of you with draw for 20 years (that is, ages 66 through 85) from the retirement accounts?

6. You buy a stock for \$1,000 and expect to sell it for \$900 after four years but also expect to collect dividends of \$120 a year.  Prove that the return on this investment is less than 10 percent.

your swift response would be greatly appreciated.

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