Q$1.$ Assume you are $27$ when you join NPS$.$ Your contributions to NPS at the end of every year $($inclusive of

employer contribution$)$ is Rs$.4$ Lakh initially, and increases every year by $6\%.$ You invest half in debt $($earning

$5\%)$ and half in equity $($earning $9\%).$ You exit at age $60.$ Assuming you use the entire accumulated corpus to

purchase a $40-$year annuity with $5\%$ return, growing at $3\%$ every year. What is the initial annual annuity

amount you receive? What is the PV of this initial amount today at $5\%$ discount rate?