At the end of each of the past 14 years, Vanessa deposited $450 in an account that earned 8 percent compounded annually. (a) How much is in the account today? (b) How much would be in the account if the deposits were made at the beginning each year rather than at the end of each year?

a) = $10,896.71

b) = $11,768.45

Explanation:

The question is divided into 2 parts

Part a) Amount in the account today

The formula to use is as follows:

FV of Annuity = P (1+r) ∧n - 1) / r

P = Periodic Payment = $450

r = Rate of each period = 8%

n = the number of periods = 14

The account today is as follows:

FV = 450 x (1+0.08) ∧14-1]/0.08

= $10,896.71

Part b) The formula to use is as follows:

FV = Future value = (1+r) * P * [ (1+r) n - 1] / r

P = Periodic Payment = $450

r = Rate of each period = 8%

n = the number of periods = 14

= Fv = (1+0.08) * 450 * [ (1+0.08) ^14 - 1] / 0.08

= $11,768.45