Hi, could you tell me if any of this statement is correct? if there is then which statement is correct? Statement I: If the annual simple interest rate equals the annual compound interest rate,then the accumulated value at any time t of an initial deposit of $X using the compoundinterest rate is always greater.Statement II : If i is unknown, then the value of d plus v cannot be determined.Statement III: ai is greater than i for all values 0 < i < 1.

Answered: Statement I: If the annual simple…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Hi, could you tell me if any of this statement is correct? if there is then which statement is correct?

Statement I: If the annual simple interest rate equals the annual compound interest rate,
then the accumulated value at any time t of an initial deposit of $X using the compound
interest rate is always greater.
Statement II : If i is unknown, then the value of d plus v cannot be determined.
Statement III: ai is greater than i for all values 0 < i < 1.

Expert Solution

Step 1

Here, the three statements are given and we have tell whether the given statements are correct or not. Here the discussion is all about the accumulated value at any time t of an initial deposit and also the compound intterest. The amount is calculated annually by the formula:

$P = {(1 + \frac{i}{n})}^{\frac{n}{t}}$

i = Nominal rate of interest, n= compounding frequency or number of compounding periods in a year.

t= Time meaning the length of tiem the interest is applicable, generally in years.

So we can determine the values and then we can say about the remaining values.