Question

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?

Answer 1

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

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`

From Simple Interest method

Simple Interest =
`(\textrm principal* \textrm rate* \textrm time)/(100)`

Or, s.i =
`(\textrm p* \textrm r* \textrm t)/(100)`

Or, s.i =
`(\textrm 500* \textrm 6* \textrm 4)/(100)`

Or, s.i =
`(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`

From Compound Interest method

Amount = Principal ×
`(1+(\textrm rate)/(100))^(\textrm time)`

Or,
`A_2` = P ×
`(1+(\textrm R)/(100))^(\textrm T)`

Or,
`A_2` = $500 ×
`(1+(\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