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- What interest rate would you need to earn in order to double your money in (a) 1 year, (b) 2 years, (c) 4 years,
(d) 6 years, (e) 8 years, (f) 12 years? - Tanya plans on retiring in 7 years. She has an investment account that she is using to save for retirement, and right now
she has about half of the amount she wants to have in the account on retirement. Assuming she makes no additional
deposits to this account, what interest rate will she need to earn in order to achieve her goal? - Laurie has $2,500 in an investment account. What annually compounded interest rate would she need to earn in order
for the account to grow to $10,000 in 20 years? - Rafael has just invested $1,000 at 8% annually compounded interest. How long will it take for this to grow to $8,000?
- Use the interest rate that you found in Exercise 19 and fi nd the future value of $2,500 at that rate in 20 years. How
good an approximation was your answer for Exercise 19? - Use the time you found in Exercise 20 and fi nd the future value of $1,000 at 8% compounded annually. How good an
approximation was your answer in Exercise 20?
E. Grab Bag- Common sense says that a high interest rate will result in more interest than a low one, and a long period of time will
result in more interest than a short one. This problem will demonstrate just how signifi cant the size of the rate and
length of time can be with compound interest.
Fill in the following table by calculating the future value of $1,000 at the interest rate given by the row and the period
of time given by the column. For example, the fi rst entry, which is fi lled in for you, gives the future value of $1000 in
5 years at 3% compound interest.
5 years 10 years 20 years 40 years3%
6%
9%
12%- An alternative way of looking at the effect of time and rate would be to look at things from the point of view of
accumulating a specifi c target future value. The higher the rate and the longer the time, the less money you need to
deposit in order to achieve the same result.
Fill in the table below by calculating the present value needed to grow to $100,000 at the interest rate given by the row
and the period of time given by the column. For example, the fi rst entry is fi lled in for you, showing the amount needed
to grow to $100,000 in 5 years at 3% compound interest.
5 years 10 years 20 years 40 years3% $86,260.88
6%
9%
12%Exercises 3.1 99