APPLICATIONS OF EXPONENTIAL AND
LOGARITHMIC FUNCTIONS

(Interest Rate Word Problems)

1. To solve an exponential or logarithmic word problems, convert the narrative to an equation and solve the equation.

Example 3: You are trying to decide whether to deposit your $1,000 in Bank A, Bank B, Bank C, Bank D, or Bank E. You want to leave your money in the bank for 5 years and you want to maximize your ending balance.
Bank A pays 15% simple interest; Bank B pays 14% interest compounded monthly; Bank C pays 13.3% interest compounded quarterly; Bank D pays 13% interest compounded continuously; and Bank E pays 13.5% interest compounded weekly.
Which bank pays the most and which bank pays the least? In which bank will you deposit your money? What is the effective interest rate of each of the banks?

Explanation and Solution:

  • Bank A: Simple interest means that there is no compounding. At the end of the five years, you will have your initial $1,000 plus the interest earned on the $1,000. The interest is calculated by multiplying the interest rate, 15%, by the number of years, 5. Therefore, the interest earned is tex2html_wrap_inline235 . You will have

    displaymath237

    at the end of the five years.
    The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years

    displaymath239

    or

    displaymath241

    which gives

    displaymath243

    displaymath245

    displaymath247

    displaymath249

    displaymath251

    hence

    displaymath253

    This means that although the bank is quoting a high interest rate of 15%, in reality, the effective interest rate is only 11.84%

  • Bank B: This bank pays 14% interested compounded monthly. This means that the interest is paid every month on the balance in the account. Or, the interest is paid 12 times a year for 5 years. Your balance will be

    displaymath255

    or

    displaymath257

    at the end of the five years.
    The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years

    displaymath259

    or

    displaymath261

    which gives

    displaymath263

    displaymath265

    displaymath267

    displaymath269

    displaymath271

    hence

    displaymath273

    This means that although the bank is quoting a 14% interest rate, in reality, the effective interest rate is a little higher at 14.93.%

  • Bank C: This bank pays 13.3% interest compounded quarterly. This means that the interest is paid every quarter on the balance in the account. Or, the interest is paid 4 times a year for 5 years. Your balance will be

    displaymath275

    at the end of the five years.
    The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years

    displaymath277

    displaymath279

    displaymath281

    displaymath283

    displaymath285

    displaymath287

    displaymath289

    which gives

    displaymath291

    This means that although the banks is quoting a 13.3% interest rate, in reality, the effective interest rate is a little higher at 13.98%

  • Bank D: This bank pays 13% interested compounded continuously. This means that the interest is calculated and paid continuously on the balance in the account. Your balance will be

    displaymath293

    at the end of the five years.
    The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years

    displaymath295

    displaymath297

    displaymath299

    displaymath301

    displaymath303

    displaymath305

    displaymath307

    which gives

    displaymath309

    This means that although the banks is quoting a 13% interest rate, in reality, the effective interest rate is a little higher at 13.88%

  • Bank E: This bank pays 13.5% interested compounded weekly. This means that the interest is paid every week on the balance in the account. Or, the interest is paid 52 times a year for 5 years. Your balance will be

    displaymath311

    or

    displaymath313

    at the end of the five years.
    The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years

    displaymath315

    displaymath317

    displaymath319

    displaymath321

    displaymath323

    displaymath325

    displaymath327

    which gives

    displaymath329

    This means that although the banks is quoting a 13.5% interest rate, in reality, the effective interest rate is a little higher at 14.43%

    To recap: The effective interest rates of Banks A, B, C, D, and E are: 11.84%, 14.93%, 13.98%, 13.88%, and 14.43%, respectively. It appears that Bank B pays the most and Bank A pays the least.

  • If you would like to work a problem and review the answer and solution, click on Problem.

    [Previous Example] [Menu Back to Applications]

    [Algebra] [Trigonometry] [Complex Variables]

    S.O.S MATHematics home page

    Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

    Author: Nancy Marcus

    Copyright 1999-2017 MathMedics, LLC. All rights reserved.
    Contact us
    Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
    users online during the last hour