Question

Sally Prescott plans on retiring in 15 years, that is, she will work for another 15 full years. When she retires she plans on spending 3 years in Bulgaria volunteering for the Peace Corps. After which she will spend her time in Boca Raton, Florida at a townhouse she purchased 5 years ago for $250,000. She currently has $100,000 in savings. She estimates that she will need $20,000 a year for living expenses in Bulgaria and then $35,000 a year for approximately 20 years when she retires to Florida. If she earns 4% compounded monthly in her savings account, how much must she deposit each year to meet her financial goals? She will withdraw her annual cash flows at the beginning of each year, that is, her first $20,000 withdrawal will occur at the beginning of year 16, before she travels to Bulgaria. Her annual deposits will begin at the end of this year and continue until she leaves for Bulgaria.

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+4/(12*100))^12-1)*100

Effective Annual Rate% = 4.0742

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 20000*((1-(1+ 4.0742/100)^-3)/(4.0742/100))*(1+4.0742/100)

PV = 57681.83

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 35000*((1-(1+ 4.0742/100)^-20)/(4.0742/100))*(1+4.0742/100)

PV = 491804.07

Future value = present value*(1+ rate)^time

491804.07 = Present value*(1+0.040742)^3

Present value = 436277.56

total amount needed just before retirement = 436277.56+57681.83=493959.39

Future value = present value*(1+ rate)^time

Future value = 100000*(1+0.040742)^15

Future value = 182031.36

Amount to be financed by yearly deposit = 493959.39-182031.36=311928.03

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

C = Cash flow per period

i = interest rate

n = number of payments

311928.03= Cash Flow*(((1+ 4.0742/100)^15-1)/(4.0742/100))

Cash Flow = 15492.33