Question

Cassidy has saved $8,000 this year in an account that earns 9% interest annually. Based on the rule of 72, it will take about years for her savings to double.

Answer 1

Answer:

The number of years in which saving gets double is 8 years .

Step-by-step explanation:

Given as :

The principal amount saved into the account = p = $8,000

The rate of interest applied = r = 9%

The Amount gets double in n years = $A  

Or, $A = 2 × p = $8,000 × 2 = $16,000

Let the number of years in which saving gets double = n years

Now, From Compound Interest method

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, 2 × p = p × $(1+\dfrac{\textrm r}{100})^{\textrm n}$

Or, $16,000 = $8,000 × $(1+\dfrac{\textrm 9}{100})^{\textrm n}$

Or, $\dfrac{16,000}{8,000}$ = $(1.09)^{n}$

Or, 2 = $(1.09)^{n}$

Now, Taking Log both side

$Log_{10}$2 = $Log_{10}$ $(1.09)^{n}$

Or, 0.3010 = n × $Log_{10}$1.09

Or, 0.3010 = n × 0.0374

∴ n = $\dfrac{0.3010}{0.0374}$

I.e n = 8.04 ≈ 8

So, The number of years = n = 8

Hence, The number of years in which saving gets double is 8 years . Answer