My sister turned 35 today and she is planning to save $5,000 per year for retire

Question

My sister turned 35 today and she is planning to save $5,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that will provide a return of 8% per year. She plans to retire 30 years from today when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend in each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

Note: Please show work using financial calculator in TVM (PV, PMT, I/Y, FV, N)

Explanation / Answer

This has 2 parts : 1. We have to calculate future value of an annuity of $5000 for 30 yrs @8%. This will be her retirement egg. 2. Then she will withdraw PMT from this egg for 25 Yrs at the end of which the egg wil become zero. In absence of info, lets assume that the lump sum egg will continue to earn interest at 8% pa. Part 1: Here FVA = PMT(FVIFAi,n). ie. FVA = PMT*[(1+i)^n-1]/i Here PMT = $5000, i=8%, n=30 Putting values we get FVA = 5000*((1+8%)^30 - 1)/8% = 5000*(10.0626-1)/8% = $566,416.06 So at end of 30 yrs, she will have her retrmnt egg corpus as $566,416.06 Part 2: Here we need to calculate PV of Annuity. PVA = $566,416.06, PMT = ??, n=25 yrs, INT i=8% Present value of annuity PVA = PMT(PVIFAi,n). So PVA = PMT*(1/i - 1/(i(1+i)^n)) So we get PVA = PMT*(1/8% -1/(8%*(1+8%)^25)) ie PVA = PMT*(12.5 -1.8522) = PMT*10.6478 = $566,416.06 So PMT = $566,416.06/10.6478 = $53195.59 So she can wthdraw $53,159.59 every year for 25 yrs.

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.