Answer to Question #124767 in Finance for yash moryani

Question

Neha would retire 30 years from today and she would need ₹ 6,00,000 per year after her retirement, with the first retirement funds withdrawn one year from the day she retires. Assume a return of 7% per annum on her retirement funds and if her planning is for 25 years after retirement,
Calculate:
a. How much lumpsum she should deposit in her account today so that she has enough funds for retirement?
b. How much she should deposit each year so that she has enough funds for retirement?

Answer 1

a. Lump sum to deposit in her account today

Workings

Yearly interest rate = 7% ~ 0.07

Amount required after retirement = ₹600,000

No of years for which payment is required = 25 years

Rate of return required i = 7% = 0.07

Present Value

PV = PMT/i * (1-(1+i)^-n)

PV =$600,000/0.07 \times (1-(1+0.07)^{-25})$

PV = $8,571,428.57 \times (1-(1+0.07)^{-25})$

PV = $8,571,428.57 \times (1 - 0.184249178)$

PV = 8,571,428.57 * 0.815750822

PV = ₹ 6,992,149.91

Amount required to be invested now (year 0)

A = PV * Present value annuity factor (PVIF)

PVIF

i = 7% = 0.07

n = 30 years

PVIF = (1+i)^-n

PVIF = $(1+0.07)^{-30}$

PVIF = $1.07^{-30}$

PVIF = 0.131367117

Amount = $6,992,149.91 \times 0.131367117$

Amount = ₹ 918,538.58

b. Amount to deposit each year

N= 25 years

i=0.07

FV= $600,000 / 0.07 \times (1-(1+0.07)^{-25})$

FV = ₹ 6,992,149.91

FV = $PMT/i \times [(1+i)^n – 1]$

6,992,149.91 = $PMT/0.07 \times [(1+0.07)^{30} – 1]$

6,992,149.91 = $PMT/0.07 \times [7.612255 - 1]$

6,992,149.91 = $PMT/0.07 \times 6.612255$

6,992,149.91 = $PMT \times 94.46079$

PMT = 6,992,149.91 / 94.46079 = 74,021.72

Amount to deposit each year = ₹74,021.72 per year