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×(1−(1+0.07)−25)
PV = 8,571,428.57×(1−(1+0.07)−25)
PV = 8,571,428.57×(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 = 6,992,149.91×0.131367117
Amount = ₹ 918,538.58
b. Amount to deposit each year
N= 25 years
i=0.07
FV= 600,000/0.07×(1−(1+0.07)−25)
FV = ₹ 6,992,149.91
FV = PMT/i×[(1+i)n–1]
6,992,149.91 = PMT/0.07×[(1+0.07)30–1]
6,992,149.91 = PMT/0.07×[7.612255−1]
6,992,149.91 = PMT/0.07×6.612255
6,992,149.91 = PMT×94.46079
PMT = 6,992,149.91 / 94.46079 = 74,021.72
Amount to deposit each year = ₹74,021.72 per year
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