Question

If you deposit $10,000 in an investment account today, it can double in value to $20,000 in just a couple of decades even at a relatively low interest rate (say, 4%).

Answer 1

In this question, We have to compure the Rate of Interest (r) so that we can compare it with the given rate of of 4%. In this question, information is as follows.

Step1: Arrenge information as given below.

The Principal Amount P= $10,000, and Future Value of Money (F.V) is $20,000 and Time is 2 Decades. 2 Decades= 20 years. So, We have to Find out Intersest rate (i) at which P will double.

Step2: Apply the folling Formula

F.V = P (1+ r)ⁿ

20,000 = 10,000 (1+ r)²⁰

20,000/10,000 = (1+r)²⁰  

2 = (1+ r)²⁰

Step3:  

Now remove the exponent or power by Multiplying both side 1/20 as follows.

(2)^1/20 = [ (1+ r )^{20 1/20} [20 1/20 = 1]

2^1/20 = 1+ r

Step4:

Find out value of 2^1/20 with the help of scientific calculator

2 x^y (120) = 1.03526

1.03526 = 1+ r

r = 1.03526 - 1

= 0.03526= 3.526%

Thus, $10,000 will become $20,000 in 20 years or 2 decades at 3. 526% which is ralatively lower than 4%.