Work These If You Did Not Get 1A Correct

Math 370

Sample Questions in Preparation for Test 2

1. Calculate the accumulated value of an annuity that pays 200 at the beginning of each year for 5 years at a nominal interest rate of 8% compounded quarterly.
2. Calculate the present value of an annuity immediate that pays $100 monthly for 5 years at an annual effective rate of interest of 12%.
3. An annuity pays $100 at the end of one month. It pays $110 at the end of the second month. It pays $120 at the end of the third month. The payments continue to increase by $10 each month until the last payment is made at the end of the 36th month. Find the present value of the annuity at 9% compounded monthly.
4. An annual annuity due pays $1 at the beginning of the first year. Each subsequent payment equals 105% of the prior payment. The last payment is at the beginning of the 10th year. Calculate the present value at:
5. An annual effective interest rate of 4%;
6. An annual effective interest rate of 5%.
7. An annuity pays $100 at the end of each month in the first year, $200 at the end of each month in the second year, and continues to increase until it pays 1000 at the end of each month during the 10 year. Calculate the present value of the annuity at an annual effective interest rate of 6%.
8. A monthly annuity due pays $1 at the beginning of the first month. Each subsequent payment increases by $1. The last payment is made at the beginning of the 240th month. Calculate the accumulated value of the annuity at the end of the 240th month using:
9. An interest rate of 6% compounded monthly;
10. An annual effective interest rate of 6%.
11. A perpetuity pays $100 at the end of the first year. Each subsequent annual payment increases by $50. Calculate the present value at an annual effective interest rate of 10%.
12. Calculate the present value of a continuous annuity of 1000 per annum for 8 years at:
13. An annual effective interest rate of 4%;
14. A constant force of interest of 4%.
15. Calculate the present value at an annual effective interest rate of 6% of a 10 year continuous annuity which pays at the rate of t2per period at exact moment t.
16. An annuity pays 10 at the end of year 2, and 9 at the end of year 4. The payments continue decreasing by 1 each two year period until 1is paid at the end of year 20. Calculate the present value of the annuity at an annual effective interest rate of 5%.

1. An investment project has the following cash flows:

1. Calculate the Net Present Value at 15%.
2. Calculate the internal rate of return on this investment.

1. 100 is invested in a Fund A now. Fund A will pay interest at 10% each year. When the interest is paid in Fund A, it will be immediately removed an invested in Fund B paying 8%. Calculate the total in Fund A and Fund B after 10 years.
2. Clinton pays 1000 at the beginning of each year into a fund which earns 6%. Any interest earned is reinvested at 8%. Calculate the total that Clinton will have at the end of 7 years.
3. A fund has 10,000 at the start of the year. During the year $5000 is added to the fund and $2000 is removed. The interest earned during the year is $1000. Which of the following are true:
4. The amount in the fund at the end of the year is $14,000.
5. If we assume that any deposits and withdrawals occur uniformly throughout the year, i is approximately 8.33%.
6. If the deposit was made on April 1 and the withdrawal was made on August 1, then i is approximately 7.74%.

(a)Only Item i is true.

(b)Only Item i and ii are true

(c)Only Item i and iii are true

(d)All three Items are true

(e)The correct answer is not given by (a), (b), (c), or (d).

1. Which of the following are true?
2. Time weighted rates of interest will always be higher than dollar weighted rates of interest.
3. Dollar weighted rate of interest provide better indicators of underlying investment performance than do time weighted rates of interest.
4. Dollar weighted rates of interest provide a valid measure of the actual investment results.

(a) Only Item ii is true

(b)Only Item i and ii are true

(c)Only Item ii and iii are true

(d)All three Items are true

(e)The correct answer is not given by (a), (b), (c), or (d).

1. A fund has 1000 at beginning of the year. Half way through the year, the fund value has increased to 1200 and an additional 1000 is invested. At the end of the year, the fund has a value of 2000.
2. Calculate the exact dollar weighted rate of return using compound interest.
3. Calculate the estimated dollar weighted rate of return using the assumptions that 1-tit = (1-t)i.
4. Calculate the time weighted rate of return.
5. The following table lists the interest rate credited under an investment year method of crediting interest.

Becky invests $1000 on January 1, 1999 and an additional $500 on January 1, 2003. How much money does Becky have on December 31, 2004.

Answers

1. 1278.33
2. 4558.78
3. 8394.60
4. a. 42.77

b.36.00

1. 45,561.83
2. a. 78,761.45

b.78,761.45

1. 6000
2. a. 6.866

b.6.846

1. 216.74
2. 38.25
3. a. -55.51

b.7.49%

1. 244.87
2. 8977.47
3. C
4. E
5. a. 6.70%

b.7.14%

1. 14.55%

1. 1976.88