Download Double Your Money!!

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Double Your Money!!
Instructions: In this project, you will explore the relationship between an interest rate and the time it takes for your money to double. Assume that all
interest is compound interest that is compounded annually. During
your calculations, please round to 5 decimal places. Round your answers to
2 decimal places. As always, please show all work.
Due: Wednesday, October 24th
1) Consider these three options for savings accounts:
Bank
Int. rate
Plum Savings
7%
Folk’s Bank
5%
Business Mutual
3.5%
a) Rachel has $375. How long would it take for her to double this amount
using each of the banks above?
(Please convert decimals to percents before rounding for your final answer)
(i) Plum Savings:
(ii) Folk’s Bank:
(iii) Business Mutual:
b) How long would it take Zach to double his $20,000 in each of the three
banks?
(i) Plum Savings:
(ii) Folk’s Bank:
(iii) Business Mutual:
2) Suppose Second Union Bank advertises that they will take $5,000 today and give you
back $10,000 in 95 months. What interest rate are you earning? Is this a good deal
compared to the three banks in # 1?
3) Using your results from #1, does the amount of principal affect the relationship between
the interest rate and the time required to double your investment?
4) Let’s see if we can find a pattern. For each situation above, multiply the interest rate
(this time as a percent) by the time (in years) it takes for the money to double. (For
example, if I found the rate to be 2.4% and the doubling time to be 15 years, I would do
2.4 ∗ 15)
Hint: The numbers you get should be pretty close to each other
Bank
(Int. rate) ∗ (time)
Plum Savings
Folk’s Bank
Business Mutual
Second Union
These values are all close to:
(choose a nice round number)
5) Explain how we can use this relationship to roughly estimate the number of years it would
take to double your principal, given a specific interest rate. For example, show how we
could easily approximate how many years this would take if the interest rate was 2%, 6%,
or 10%.