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)
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