1.Two investments are made at the same time. The first consists of investing 1550 dollars at a nominal rate of interest of 7.9 percent convertible semiannually. The second consists of investing 1450 dollars at a nominal rate of interest of 7.9 percent convertible daily. How long will it take for the two investments to be worth exactly the same amount? (Assume compound interest at all times)
2. Xena invests 4000 dollars in an account paying 10.7 percent interest convertible monthly. How long will it take for her account balance to reach 9200 dollars? (Assume compound interest at all times.)
3. Your cousin Ray borrows 1300 dollars now, repays 750 dollars in two years, and then borrows 1000 dollars in another three years, all at nominal rates of interest of 9.4 percent convertible quarterly. Your other cousin Jay borrows 1550 dollars t years from now at the same interest rate. If the present value of both of your cousin's debts is the same, what is t? (Assume compound interest at all times.)
4. Rhonda deposits A dollars in an account paying 8.2 percent effective, and at the same time also deposits B dollars in another account paying 9.2 percent effective. After 9 years have passed, the combined total in the two accounts is 55000 dollars. In another 3 years, the balance in the account paying 9.2 percent effective is three times that of the other account. What is the balance in the account paying 8.2 percent effective 15 years after the initial deposit?
5. Cicely invests 3800 dollars in an account paying an effective rate of interest of 5.3 percent. Two years later, she deposits an additional 1400 dollars. If there are no other transactions, how long will it take (from the time of the first investment) for her account balance to reach 8600 dollars? (Assume simple interest between compoundings.)
6.Suppose that you open a mutual fund account with a deposit of 525 dollars. 5 months later, the fund balance is 590 dollars, and you withdraw 216 dollars. A year after the account was opened, your balance is X dollars. If the dollar weighted and time weighted rates of return were the same, what is the rate of return? (Assume simple interest for the dollar weighted calculation.)
7. Your grandmother gives you 3800 dollars for your birthday, which you invest in a mutual fund on January 1. On June 1, your fund balance is 7800 dollars, and you then deposit 1100 dollars (which you received for your high school graduation). On the following January 1, you calculate that your dollar-weighted rate of return for the year was 33.2 percent. What was your time-weighted rate of return for the year?
8.Your grandmother gives you 370 dollars for your birthday, which you invest in a mutual fund on January 1, 2002. On June 1, 2002, she gives you 690 dollars for your high school graduation, which you immediately deposit into your mutual fund. On January 1, 2003, you take out your calculator and find that your dollar weighted rate of return for the previous year was 8.2 percent. On April 1, 2003 your fund balance is 1000 dollars and you then deposit your grandmother's Easter gift of X dollars. On January 1, 2004, your fund balance is 2000 dollars and you calculate that your time weighted rate of return for the previous year was 10 percent. What is X? (As usual, assume simple interest for the dollar weighted rate of return, and months of equal length.)
9.Wendel invests 6800 dollars in a mutual fund on January 1. On June 1, his fund balance is 3000 dollars. Wendel notices the decline, and withdraws 1300 dollars. On September 1, his fund balance is 7000 dollars, and he then invests an additional 1300 dollars. On the following January 1, his fund balance is 7200 dollars. What is Wendel's time-weighted rate of return?
10.Jeff invests 7700 dollars in a mutual fund on June 1. On October 1, his fund balance is 3100 dollars, and he deposits 1400 dollars. On the following June 1, his fund balance is 2500 dollars. What is Jeff's time-weighted rate of return?
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