Question

An initial deposit of $50 is made into an account that had a 5% interest rate compounded annually. Which expression

shows the amount of money in the account after tyears?

Answer 1

The Amount of money in the account after t years $50
`(1.05)^(t)`

Explanation:

Given as :

The principal deposited into account = $50

The rate of interest = 5% compounded annually

The time period for deposit = t years

Let the amount into account after t years = $A

now, According to question

From compound Interest method

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

Or, A = $50 ×
`(1+(\textrm r)/(100))^(\textrm t)`

Or, A = $50 ×
`(1+(\textrm 5)/(100))^(\textrm t)`

Or, A = $50 ×
`(1.05)^(t)`

or, A = $50
`(1.05)^(t)`

So, The amount in account after t years = A = $50
`(1.05)^(t)`

Hence, The Amount of money in the account after t years $50
`(1.05)^(t)` . Answer