1. For the following problems, determine how many years it will take for the two accounts to reach the same amount.
A 1000 dollar investment at a rate of 3% compounded monthly and an 1100 dollar investment at a rate of 3.02% compounded annually.
A 2000 dollar investment at a rate of 4% compounded continuously and a 3000 dollar investment at a rate of 5% compounded monthly.
2. Calculate the annual percentage yield for each investment.
A. A savings account paying an annual rate of 4 percent compounded quarterly.
B. A checking account paying an annual rate of 1.5 percent compounded daily.
3.What is the future value if $4900 is invested for 3 years at an annual rate of 12% compounded monthly?
4. What is the annual percentage yield (or effective annual rate) for a nominal rate of 7.3% compounded quarterly?
Solution Preview
Problem #1
(a) Suppose after t years, the two accounts reach the same amount.
For the first account with $1000, after t years, its balance is
1000 * (1 + 0.03/12)^(12t) = 1000 * 1.0025^(12t)
For the second account with $1100, after t years, its balance is
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