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

The statement Shelly will have $11.2 more in her account than Anne is correct statement .

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 =
`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 = $120

∵, Amount = Principal + interest

Or,
`A_1` = p + s.i

Or,
`A_1` = $500 + $120

Or,
`A_1` = $620

So,The amount in account after 4 years =
`A_1` = $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 =
`A_2`

From Compound Interest method

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

Or, Amount = 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 × 1.2624

∴
`A_2` = $631.2

So,The amount in account after 4 years =
`A_2` = $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