Comparing Account Balances In Exercise, $2000 is deposited in an account. Decide which account, (a) or (b), will have the greater balance after 10 years.

(a) 6 1/2%, Compounded monthly

(b) 6 1/4%, Compounded continuously

Answer:account b will have the greater balance after 10 years.

Step-by-step explanation:

a) $2000 is deposited in an account. This means that the principal,

P = 2000

It was compounded monthly. This means that it was compounded 12 times in a year. So

n = 12

The rate at which the principal was compounded is 6.5%. So

r = 6.5/100 = 0.065

It was compounded for just 10 years. So

t = 10

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 = 2000 (1+0.065/12) ^12*10

A = $3824

b) The formula for continuously compounded interest is A = P x e (r x t)

Where

e = 2.7183

A = 2000 * 2.7183^ (0.0625 * 10)

A = $3736.5