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kari74 [83]
3 years ago
5

Anne deposited $500 in an account that earns 6% simple annual interest. Shelly deposited $500 in an account that earns 6% annual

interest compounded annually. They leave the money in the account for 4 years. Which statement is true about the two investments after 4 years?
Mathematics
1 answer:
Inga [223]3 years ago
8 0

Answer:

It is clear that, The Shelly account is $11.23 more than that in Anne account .

Step-by-step explanation:

Given as :

For Anne

The amount deposited in account = p = $500

The rate of interest = r = 6%  at simple interest

The time period of deposit = t = 4 years

Let The amount received in account after 4 years = $A_1

<u>From Simple Interest method</u>

Simple Interest = \dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}

Or, s.i = \dfrac{\textrm p\times \textrm r\times \textrm t}{100}

Or, s.i = \dfrac{\textrm 500\times \textrm 6\times \textrm 4}{100}

Or, s.i = \dfrac{12000}{100}

i.e s.i = $120

∵ Amount = Principal + Interest

Or, A_1 = p + s.i

Or A_1 = $500 + $120

Or, Amount = $620

So, The Amount in Anne account after 4 years is $620

Again

For, Shelly

The amount deposited in account = P = $500

The rate of interest = R = 6% compounded annually

The time period of deposit = T = 4 years

Let The amount received in account after 4 years = $A_2

<u>From Compound Interest method</u>

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

Or, A_2 = P × (1+\dfrac{\textrm R}{100})^{\textrm T}

Or, A_2 = $500 × (1+\dfrac{\textrm 6}{100})^{\textrm 4}

Or, A_2 = $500 × (1.06)^{4}

Or, A_2 = $500 × 1.26247

Or, A_2 = $631.23

So, The amount received by Shelly in her account after 4 years = $631.23

Now, Difference between amount received in their account

i.e  A_2 -  A_1 = $631.23 - $620

Or, A_2 -  A_1 = $11.23

Hence, It is clear that, The Shelly account is $11.23 more than that in Anne account . Answer

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