Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Note Some of the formulas below use the special number
What if Interest is Compounded More Often than Monthly? Some lending institutions compound interest daily or even continuously. (The term continuous compounding is used when interest is being added as often as possible-that is, at each instant in time.) The point of this exercise is to show that, for most consumer loans, the answer you get with monthly compounding is very close to the right answer, even if the lending institution compounds more often. In part
a. Would you expect your monthly payment to be higher or lower if interest were compounded daily rather than monthly? Explain why.
b. Which would you expect to result in a larger monthly payment, daily compounding or continuous compounding? Explain your reasoning.
c. When interest is compounded continuously, you can calculate your monthly payment
where
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- You invest $6000 at an annual rate of 4. Find the balance after 7 years for each type of compounding. a.Quarterlyb.Monthlyc.Continuousarrow_forwardFuture Value Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of r as a decimal, then the value of the investment after t years is given by FutureValue=P1+rt. In this formula, 1+rt is known as the future value interest factor, so the formula above can be written as FutureValue=PFuturevalueinterestfactor Financial officers normally calculate this or look it up in a table a. What future value interest factor will make an investment double? b. Say you have an investment that is compounded yearly at a rate of 9%. Find the future value interest factor for a 7-year investment. c. Use the results from part b to calculate the 7-year future value if your initial investment is 5000.arrow_forwardYou invest $6000 at an annual rate of 4. Find the balance after 7 years for each type of compounding. a. Quarterly b. Monthly c. Continuousarrow_forward
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