Question

1.. Suppose $2000 is invested at 6% annual interest rate for 10 years and the interest is compounded monthly. How much will the investment be worth at the end of the 10 years?

2. Suppose John invests his tax refund of $1666 in an account that earns interest compounded continuously at the rate of 3.5%. How much will John have in 7.5 years? Show your work details.

3. What is the present value of an account that will be worth $10,000 in 5 years if the annual interest rate is 10% and the interest is compounded continuously? Show your work details.

4.A company shows the following profit figures for the years 2000, 2004, and 2008. In 2000 the profit was $250 million; in 2004, the profit was $400 million; and, in 2008, the profit was $550 million. If x is the number of years after 2000, write a linear function representing this profit. Using this linear model determine what the projected profit will be in the year 2020. Show work details.

5. The table shows the year and the number of people unemployed in a particular city for several years. Determine whether the trend appears to be approximately linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 15 people?

Year                          1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Number Unemployed 750   670   650   605   550   510   460   420   380   320

6. Wilbur and Cody are selling pies for a school fundraiser. Customers can buy cherry pies and blackberry pies. Wilbur sold 8 cherry pies and 2 blackberry pies for a total of $110. Cody sold 7 cherry pies and 6 blackberry pies for a total of $177. What is the cost each of one cherry pie and one blackberry pie? Show work details.

Answer 1

1. We can use financial calculator to get the investment's future value in 10 years.

Interest is compounded monthly. so, we need to convert 10 years in to months and coupon interest and coupon rate also be monthly.

PV = present value = $2000; I/Y = coupon rate = 6%/12 = 0.5%; PMT = coupon = $2000*6%/12 = $10; N = no. of months = 10*12 = 120 > CPT = compute > FV = future value = $5277.59

2. Future value of investment with interest continuously compounded.

Future value = present value*e^rt

Present value is $1666. r is interest rate 3.5% and t is time 7.5 years.

Future value = $1666*e^0.035*7.5 = $1666*1.3002 = $2,166.13

Value of e^0.035*7.5 can be calculated using financial calculator. 0.035*7.5 = 0.2625. enter 0.2625 in the calculator and then press first 2ND key and then LN key. you will get 1.3002.

3. Present value of investment with interest continuously compounded.

Present value = Future value/e^rt

Future value is $10,000. r is interest rate 10% and t is time 5 years.

Present value = $10,000/e^0.10*5 = $10,000/1.6487 = $6,065.38

Value of e^0.10*5 can be calculated using financial calculator. 0.10*5 = 0.5. enter 0.5 in the calculator and then press first 2ND key and then LN key. you will get 1.6487.