Respuesta :
Answer:
The statement Shelly will have $11.2 more in her account than Anne is correct statement .
Step-by-step explanation:
Given as :
For Anne
The principal deposited in account = $500
The rate of interest = r = 6 % at simple interest
The time period = t = 4 years
Let The amount in account after 4 years = [tex]A_1[/tex]
From Simple Interest method
Simple Interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]
Or, s.i = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]
Or, s.i = [tex]\dfrac{\textrm 500\times \textrm 6\times \textrm 4}{100}[/tex]
Or, s.i = $120
∵, Amount = Principal + interest
Or, [tex]A_1[/tex] = p + s.i
Or, [tex]A_1[/tex] = $500 + $120
Or, [tex]A_1[/tex] = $620
So,The amount in account after 4 years = [tex]A_1[/tex] = $620
Again
For Shelly
The principal deposited in account = $500
The rate of interest = r = 6 % at compounded annually
The time period = t = 4 years
Let The amount in account after 4 years = [tex]A_2[/tex]
From Compound Interest method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, Amount = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, [tex]A_2[/tex] = $500 × [tex](1+\dfrac{\textrm 6}{100})^{\textrm 4}[/tex]
Or, [tex]A_2[/tex] = $500 × [tex](1.06)^{4}[/tex]
Or, [tex]A_2[/tex] = $500 × 1.2624
∴ [tex]A_2[/tex] = $631.2
So,The amount in account after 4 years = [tex]A_2[/tex] = $631.2
Now, Difference between amount in both accounts
i.e Amount into Shelly account - Amount into Anne account = $631.2 - $620
Or, Difference between amount in both accounts = $11.2
∴ It is now clear that amount in credited into Shelly account is $11.2 more
Hence, The statement Shelly will have $11.2 more in her account than Anne is correct statement . Answer
