Question

2. A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.

(a) Write an equation to represent the amount of money in the account as a function of time in years.


(b) Find the amount of time it takes for the account balance to reach $800. Show your work.

Answer 1

Explanation:

Initial amount that was deposited into the savings account is $600 This means that the principal,

P = 600

The account earns 2.1 % interest compounded annually.. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 2.1%. So

r = 2.1/100 = 0.021

It was compounded for t years. So

t = t

a) The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 600 (1+0.021/1)^1×t

A = 600(1.021)^t

b)when A =$800, it becomes

800 = 600(1.021)^t

Dividing both sides by 600, it becomes

1.33 = (1.021)^t

Taking the tth root of both sides

t = 14 years

It will take 14 years