Chapter MPS, Problem 9.10MPS

(a)

To determine

To find: The expression for both accounts earn the same amount of interest.

Answer to Problem 9.10MPS

  $\frac{\left(\$50000-x\right)\times 13\times T}{100}$

Explanation of Solution

Given:

Deposited amount =$50000

On the tax-free account Annual interest =7%

On the money market fund the annual simple interest =13%

Formula Used:

Simple interest $=\frac{P\times R\times T}{100}$

Calculation:

Total amount deposited in two simple interest accounts $=\$50000$

Let $x$ be the amount deposited in tax-free account

Then amount deposited in market fund = $\left(\$50000-x\right)$

Let $\text{'}t\text{'}$ be the time of interest when both accounts will give the equal interest

So, after that $t$ years simple interest from tax-free account = $\frac{P\times R\times T}{100}$

= $\frac{x\times 7\times t}{100}$

And after $t$ year simple interest from market fund = $\frac{P\times R\times T}{100}$

= $\frac{\left(\$50000-x\right)\times 13\times T}{100}$

According to question

  $\Rightarrow \frac{x\times 7\times T}{100}=\frac{\left(\$50000-x\right)\times 13\times T}{100}$

Conclusion:

Thus the required expression is $\frac{\left(\$50000-x\right)\times 13\times T}{100}$ .

(b)

To determine

To find: The money invested in tax-free account so the both accounts earn the same interest.

Answer to Problem 9.10MPS

$ $32500$

Explanation of Solution

Given:

Deposited amount =$50000

On the tax-free account Annual interest =7%

On the money market fund the annual simple interest =13%

Formula Used:

Simple interest $=\frac{P\times R\times T}{100}$

Calculation:

Relation from the sub part A $\begin{array}{l}\Rightarrow \frac{x\times 7\times t}{100}=\frac{\left(\$50000-x\right)\times 13\times t}{100}\\ \Rightarrow 7x=650000-13x\\ \Rightarrow 20x=650000\\ \Rightarrow x=\frac{650000}{20}\\ \therefore x=32500\end{array}$

Conclusion:

So, money deposited in tax-free account =$32500

(c)

To determine

To find: The money invested in market fund account so the both accounts earn the same interest.

Answer to Problem 9.10MPS

  $\$17500$

Explanation of Solution

Given:

Deposited amount =$50000

On the tax-free account Annual interest =7%

On the money market fund the annual simple interest =13%

Formula Used:

  $\left(\$50000-x\right)$

Calculation:

Money deposited in market fund = $\left(\$50000-x\right)$

= $\left(\$50000-\$32500\right)$

=$17500

Conclusion:

Thus the required amount of investment is $\$17500$ .