When you were born, your dear old Aunt Minnie promised to deposit $1,000 in a saving account

Time Value of Money

Chapter # 03

Financial Management 13 Edition 

James C. Van Horne

John M. Wachowicz, Jr.

Chapter # 03 – Question # 18

Problem # 18:-    When you were born, your dear old Aunt Minnie promised to deposit $1,000 in a savings account for you on each and every one of your birthdays, beginning with your first. The savings account bears a 5 percent compound annual rate of interest. You have just turned 25 and want all the cash. However, it turns out that dear old (forgetful) Aunt Minnie made no deposits on your fifth, seventh, and eleventh birthdays. How much is in the account now – on your twenty-fifth birthday?

Solution:-

First Calculation the Future value of the entire annuity and then subtract the future values of three individual missing payments.

Future value of Annuity for 25 years:-

Formula:-

                  FV = R

• FV= Value of the annuity / Future Value of the annuity
• R = Periodic payment amount
• i/r = annual interest rate
• n/t = number of period

FV of 5^th deposit of $ 1,000 compounded for 25-5 = 20 years

FV of 7^th deposit of $ 1,000 compounded for 25-7 = 18 years

FV of 11^th deposit of $ 1,000 compounded for 25-11 = 14 years

FV = PV(1+r)ⁿ

• PV = Present Value
• i/r = annual interest rate
• n/t = number of period

Calculation:-

FVIFA of 25 Deposits=     R

R = $ 1,000

i = 5% =  = .05

n = 25

=1,000

= 1,000

=1,000

= 1,000(47.728)

= $ 47,728

FV of 5^th deposit of $ 1,000 compounded for 25-5 = 20 years

FV = PV(1+r)ⁿ

= 1,000(1+.05)²⁰

                = 1,000 (2.6533)

= $2,653.3

     FV of 7^th deposit of $ 1,000 compounded for 25-7 = 18 years

FV = PV(1+r)ⁿ

= 1,000(1+.05)¹⁸

                = 1,000 (2.4066)

= $2,406.6

FV of 11^th deposit of $ 1,000 compounded for 25-11 = 14 years

FV = PV(1+r)ⁿ

= 1,000(1+.05)¹⁴

                = 1,000 (1.9799)

= $1,979.9

Amount at the end of 25^th Birthday

=$ 47,728 – $2,653.3 – $2,406.6 -$1,979.9

= $40,688.2