Question

Betty deposits ​$300 into an account that earns 5​% interest compounded annually. Teresa deposits the same amount into an account that earns 5​% simple interest. Compare the account balances after 2 years.

Answer 1

Answer:

Step-by-step explanation:

Considering Betty's account

Initial amount deposited into the account is $300 This means that the principal is

P = 300

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 5%. So

r = 5/100 = 0.05

It was compounded for 2 years. So

t = 2

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 = 300 (1+0.05/1)^1×2

A = 300(1.05)^2 = $330.75

Considering Theresa's account,

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time

P = 300

R = 5%

T = 2

I = (300 × 5 × 2)/100 = 30

Total amount in Theresa's account after 2 years will be 30 + 300 = $330

Betty would earn more than Theresa. She will earn 330.75 - 330 = $0.75 more than Theresa.