Pre-Calculus: Compound Interest

Question

How much more would be in an account that has interest compounded continuously rather than annually if the initial deposit is $500 and the yearly interest rate is 7% for 10 years?

Answer 1

Continuously:

A₁ = Pe^rt = 500e^.7 = 1006.88

Compounded:

A₂ = P(1+r/n)^nt = 500(1+.07/1)¹⁽¹⁰⁾ = 983.58

A₁-A₂ = 1006.88-983.58 = $23.30

Answer 2

Hi Mimi L.

That can be determined by calculating the interests then subtracting the two

It could also be determined based on final value after 10 years for each option

Continously Compounded - Compounded Annually

Continuous

A = Pe^rt

A = Principal + Interest

P = Principal = 500

r = rate (written as a decimal)

t = number of years 10

Annual

FV = P(1 + r)^t

FV = Future Value = Principal + Interest

P = Principal

r = rate (written as a decimal)

t = number of years = 10

I get

1006.876 - 983.576 = 23.30

You can try it this way

Formulas for the Interest

Continously

Interest = P((e^rt - 1))

Annually

Interest = P((1+ r)¹⁰ - 1)

Remenber r should be written as a decimal in the calculation