Question

Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of 12500 dollars (starting on December 25, 2016) to supplement his income from working as a cabana boy, and he wants the money to last 10 years (i.e. he'll make 10 withdrawals total). His plan is to make annual deposits, starting on December 25, 2000 and ending on December 25, 2015, into an account paying 9.6 percent interest rate compounded annually. How large should each deposit be for Ralph to realize his goal?

Answer 1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 12500*((1-(1+ 9.6/100)^-10)/(9.6/100))

PV = 78144.85

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

78144.85= Cash Flow*(((1+ 9.6/100)^16-1)/(9.6/100))

Cash Flow = 2249.58 = yearly deposit