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Answer the following questions using the Time Value of Money table:


1. While you were a student in college, you borrowed $18,000 in student loans at an interest rate of 3 percent, compounded annually. If you repay $1,500 per year, how long, to the nearest year, will it take you to repay the loan?

2. Your client is 40 years old and wants to begin saving for retirement. You advise the client to put $6,000 a year into the stock market. You estimate that the market’s return will be, on average, 12 percent a year. Assume the investment will be made at the end of each year. A) If the client follows your advice, how much will she have by age 65? B) if your client wants to have a pension salary (retirement salary) by age 65 and forever, how much the yearly salary is, assuming that the interest rate at that date = 5%?

3. Adams Company bought a piece of land in 1981 for $200,000. By 2005, its value had increased to $1,582,200. Find the annual rate of appreciation during this period.

4. Your employer has promised to give you a $5,000 bonus after you have been working for him for 10 years. What is the present value of this bonus if the proper discount rate is 12%?

5. A downtown bank is advertising that if you deposit $1,000 with them, and leave it there for 60 months, you can get $1801 back at the end of this period. Assuming quarterly base compounding, what is the annual rate of interest paid by the bank?

6. Cincinnati Company has decided to put $30,000 per quarter in a pension fund. The fund will earn interest at the rate of 8% per year, compounded quarterly. Find the amount available in this fund after 10 years.

7. What is the effective interest rate for one dollar invested in the bank at a 9% nominal annual rate compounded on a daily basis ( use 365 days in a year )?

Answer :

1. According to the TVM figure, it would take roughly 13 years to pay off the $18,000 student loan with $1,500 in yearly payments and a 3% annual interest rate.

2. A) According to the TVM table, if the client follows the recommendation to invest $6,000 annually in stocks with an average return of 12%, by the time they reach 65, they will have amassed roughly $1,171,201. B) We require further information, such as the desired retirement salary, in order to calculate the annual pension salary. The required annual payment that corresponds to the future value can be determined using the TVM table in reverse, assuming a desired retirement wage, an interest rate of 5%, and a time period of 20 years. A TVM The annual pension salary amount is shown in the table. 3. We may calculate the land's annual rate of appreciation using the TVM table. The annual rate of increase is roughly 7.76% with an initial value of $200,000 and a future value of $1,582,200 over a period of 24 years. 4. The TVM table calculates the present value of the $5,000 incentive to be roughly $1,280 using a 12% discount rate and a 10-year time horizon. 5. We can get the annual interest rate the bank pays by using the TVM table. With a time frame of 60 months (or 15 quarters), a present value of $1,000, a future value of $1,801, and quarterly compounding, the The bank charges an annual interest rate of about 11.18%. 6. With a quarterly deposit of $30,000, an interest rate of 8% per year compounded quarterly, and a time frame of 40 quarters, we can use the TVM table to calculate the amount that will be accessible in the pension fund after 10 years. The value is estimated to be around $485,884 by the TVM table. 7. We can use the TVM table or the previously given formula to determine the effective interest rate for a dollar invested in a bank at a nominal annual rate of 9% compounded daily (365 days in a year). According to the methodology, the actual interest rate is around 9.60%.

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