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

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

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+(\textrm rate)/(100))^(\textrm time)`

Or, 2 × p = p ×
`(1+(\textrm r)/(100))^(\textrm n)`

Or, $16,000 = $8,000 ×
`(1+(\textrm 9)/(100))^(\textrm n)`

Or,
`(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 =
`(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