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1. How long will it take a $500 investment to be worth $700 if it is continuousl

ID: 2836084 • Letter: 1

Question

1. How long will it take a $500 investment to be worth $700 if it is continuously compounded at 9% per year? (Give the answer to two decimal places.)

2. How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 15% per year?

3. How long, to the nearest year, will it take me to become a millionaire if I invest $3000 at 12% interest compounded continuously?

4. This exercise is based on the following table, which lists interest rates on long-term investments (based on 10-year government bonds) in several countries in 2011.

Assuming that you invest $9,000 in the U.S., how long (to the nearest year) must you wait before your investment is worth $19,000 if the interest is compounded annually?

5. This exercise is based on the following table, which lists interest rates on long-term investments (based on 10-year government bonds) in several countries in 2011.

If the interest on a long-term U.S. investment is compounded continuously, how long will it take the value of an investment to double? (Give the answer correct to 2 decimal places.)

6. The rate of auto thefts doubles every 6 months.

(a) Determine, to two decimal places, the base b for an exponential model y = Abt of the rate of auto thefts as a function of time in months.

(b) Find the tripling time to the nearest tenth of a month.

7. Find N, A, and b.

8.Find N, A, and b.                

Country U.S. Japan Germany Australia Brazil Yield 3.4% 1.2% 3.3% 5.5% 12.7%

Explanation / Answer

1)
EAR = e^i -1 = 9.417%

700 = 500 * (1+0.09417)^n

n = 3.74 years


2)

EAR =e^0.15 -1 = 16.18%

3 = 1.1618^n

n = 7 years


3)

EAR = e^0.12 -1 = 12.75%

1000000 = 3000 * 1.1275^n

n = 48 years


4)

19000 = 9000 * (1+0.034)^n


n = 22 years


5)


EAR = e^0.034 -1 = 3.46%


2 = 1.0346^n

n = 20 years

6) v


b^6 = 2


b = 1.12


b)


1.12^t =3

t = 9.7 months


7)