5.2 A. Linus is 18 years old now, and is thinking about taking a 5-year university degree. The degree will cost him $25,000 each year. After he's finished, he expects to make $50,000 per year for 10 years, $75,000 per year for another 10 years, and $100,000 per year for the final 10 years of his working career. If Linus lives to be 100, and if real interest rates stay at 5% per year throughout his life, what is the equal annual consumption he could enjoy until that date?

Number of years working = 100 - 23 = 77 years

FV of investment: FVpmt = (25,000, 5n , 5%)

= $138,140.78

PV of first 10 years: PVpmt = (50,000, 10n, 5%)

= $386,086.7465

PV of second 10 years: PVpmt = (PV(5%, 20n, -1pmt) - PV(5%, 10n,-1pmt))*$75,000

=$355,535.6560

PV of second 10 years: PVpmt = (PV(5%, 30n, -1pmt) - PV(5%, 20n,-1pmt))*$100,000

=$291,024.04684

Total PV of salary = $386,086.7465 + $355,535.6560 + 291,024.04684

=$1,032,646.471

After University = $1,032,646.471 - $138,140.78

= $894,505.6909

Annual Consumption = $894,505.6909/PV(5%,77n,1pmt)

= $49,794.9338

Why is this answer calculating 77 years for equal annual income? Shouldn't it only measure for the time in retirement for consumption? 100 years - 53(working years) = 47 years of retirement..... thoughts please