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Answer:
From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days .
Step-by-step explanation:
Given as :
The principal for the first account = p = $100
The rate of interest = r = 5% compounded annually
The account gets double , so, Amount = A = $200
Let the time after which account gets double = t years
So<u>, From Compound Interest method</u>
Amount = Principal ×
As amount is double its principal
So, A = 2 × $100 = $200
Or, A = p ×
Or, $200 = $100 ×
Or, =
Or, 2 =
Taking Log both side
=
Or, 0.3010 = t
Or, 0.3010 = t × 0.0211
∴ t =
I.e t = 14.26
So, The time period to get account double is 14 years 26 days
<u>Again </u>
Amount = Principal ×
Or, A = p ×
As amount is double its principal
So, A = 2 × $1000 = $2000
Or, $2000 = $1000 ×
Or, =
Or, 2 =
Taking Log both side
=
Or, 0.3010 = t
Or, 0.3010 = t × 0.0211
∴ t =
I.e t = 14.26
So, The time period to get account double is 14 years 26 days
Hence From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days . Answer