Question

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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?

Answer 1

Amount deposited per year (Pmt) = $450

Interest rate (Rate) = 8% compounded annually

Number of years (Nper) = 14 years

Solution 1) The money is deposited at the end of the each year, so, it is the case of an ordinary annuity.

The current value in the account is calculated using FV function in Excel = FV(Rate, Nper, Pmt, PV, Type)

Since it is the case of an ordinary annuity, hence, the type would be 0.

Thus, current value in the account = FV(8%, 14, 450, 0, 0) = $10,896.71

Alternatively, it can be calculated using the below formula:

Hence, Future Value (FV) of Ordinary Annuity = 450*[(1 + 8%)^14 - 1]/8% = 450*[2.937 - 1]/8%

= 450*[1.937]/8%

= 871.737/8% = $10,896.71

Solution 2) If the deposits would be made in the account at the beginning of each year then it would be the case of annuity due.

The current value in the account is calculated using FV function in Excel = FV(Rate, Nper, Pmt, PV, Type)

Since it is the case of an annuity due, hence, the type would be 1.

Thus, current value in the account = FV(8%, 14, 450, 0, 1) = $11,768.45

Alternatively, the FV can be calculated as:

FV of Annuity Due = (1 + r)*FV of Ordinary Annuity

FV of Annuity Due = (1 + 8%)*10,896.71 = 1.08*10,896.71 = $11,768.45