Assume that you will be opening a savings account today by depositing $100,000.

Time Value of Money

Chapter # 03

Financial Management 13 Edition 

James C. Van Horne

John M. Wachowicz, Jr.

Chapter # 03 – Question # 19

Problem # 19:-    Assume that you will be opening a savings account today by depositing $100,000. The savings account pays 5 percent compound annual interest, and this rate is assumed to remain in effect for all future periods. Four years from today you will withdraw R dollars. You will continue to make additional annual withdrawals of R dollars for a while longer – making your last withdrawal at the end of year 9 – to achieve the following pattern of cash flows over time. (Note: Today is time period zero; one year from today is the end of time period 1; etc.)

How large must R be to leave you with exactly a zero balance after your final R withdrawal is made at the end of year 9? (Tip: Making use of an annuity table or formula will make your work a lot easier!)

Solution:-

100,000(FVIF_5%,3) = R(PVIFA_5%,6)

100,000(1+i)ⁿ       =  R   5.076

100,000 x (1+.05)³ = R 5.076

100,000 x 1.1576 =  R 5.076

1,15,760 = R 5.076

1,15,760/5.076 = R

$22,805.36 = R