Question

George says that an account that earns 4% interest compounded annually and an account that earns 2% interest compounded semi-annually will be worth the same if the principals are the same

Answer 1

the account won't yield the same amount despite the same principal amount.

Explanation:

To test this assertion :

Let principal = $1000

t = 1 year

Compound interest formula :

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

P = principal ; r = rate, n = number of times interest is compounded per period ; t = time

Account A :

Rate = 4% annually

A = 1000(1 + 0.04/1)^1

A = 1000 * 1.04 = $1040

Account B:

Rate = 2% compounded semianually ; n = 12 /6 = 2

A = 1000(1 + 0.02/2)^1*2

A = 1000(1.01)^2

A = 1000 * 1.0201

A = $1020.1

From the result, the account won't yield the same amount despite the same principal amount.