Answered: A company has a tax bill of $14,930…

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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Question

A company has a tax bill of $14,930 coming due in 10 months. They would like to save for this bill by depositing equal amounts each month into an account earning 5% compounded monthly. How much would they need to deposit each month in order to save for this bill? Round to 2 decimal places.

Expert Solution

Step 1: Finding the amount deposited each month

Let $$ x$ is the amount of money deposited each month

So at the end of first month, the bank account has $$ x$

Given that the rate is $5 %$ compounded monthy

At the end of second month the bank account has $= x + x (1 + \frac{5}{1200})$

At the end of third month the bank account has $= x + x (1 + \frac{5}{1200}) + x {(1 + \frac{5}{1200})}^{2}$

Proceeding this way at the end of tenth month the bank account has $= x + x (1 + \frac{5}{1200}) + x {(1 + \frac{5}{1200})}^{2} + . . . + x {(1 + \frac{5}{1200})}^{9}$

Therefore total savings in bank

$= x (1 + (1 + \frac{5}{1200}) + {(1 + \frac{5}{1200})}^{2} + . . . {(1 + \frac{5}{1200})}^{9}) = x \frac{{(1 + \frac{5}{1200})}^{10} - 1}{\frac{5}{1200}}$

Given that this amount is used to pay tax bill of $$ 14, 930$

$∴ x \frac{{(1 + \frac{5}{1200})}^{10} - 1}{\frac{5}{1200}} = 14930 \Rightarrow x ({(1 + \frac{5}{1200})}^{10} - 1) = 62.208 \Rightarrow x = \frac{62.208}{0.04245} \Rightarrow x = 1, 465.44$