Chapter 4, Problem 1Q

To determine

The present value of a dollar is more worth with 20% interest rate or 10% interest rate.

Answer to Problem 1Q

The value of a dollar is more worth today with 10% interest rate.

Explanation of Solution

Calculation of present worth of dollar when the interest rate is 20%:

Given,

Future worth is 1 dollar.

Interest rate is 20%.

Formula to calculate the present worth:

$PW=\frac{FW}{\left(1+i\right)}$

Here,

• PW is the present worth
• FW is the future worth
• iis the interest rate

Substitute 1 dollar for FW and 20% for interest rate.

$\begin{array}{c}PW=\frac{1}{\left(1+20\%\right)}\\ =\frac{1}{\left(1+0.20\right)}\\ =\frac{1}{1.20}\\ =0.83\end{array}$

Therefore, present worth of dollar, when the interest rate is 20% is 0.83.

Calculation of present worth of dollar when the interest rate is 10%:

Given,

Future worth is 1 dollar.

Interest rate is 10%.

Formula to calculate the present worth:

$PW=\frac{FW}{\left(1+i\right)}$

Here,

• PW is the present worth.
• FW is the future worth
• iis the interest rate

Substitute 1 dollar for FW and 10% for interest rate.

$\begin{array}{c}PW=\frac{1}{\left(1+10\%\right)}\\ =\frac{1}{\left(1+0.10\right)}\\ =\frac{1}{1.10}\\ =0.90\end{array}$

Therefore, present worth of dollar when the interest rate is 20% is 0.90.

The value of a dollar is more worth today with 10% interest rate.

Economics Concept Introduction

Introduction: Present worth is the current value of future money given a specified interest rate. It is also known as present discounted value. It is the value of cash today that will be received in the future. It is the worth of future amount today.