Sanjana decides to invest in a Recurring Deposit at the rate of Rs$.2,000$ per year for $5$ years and at Rs$.3000$ per year for next $10$ years. What shall be the value of her investment at the end of $15$ years, if the rate of interest is $10\%?$

If she wants to receive a lumpsum payment of Rs$.1,00,000$ at the end of $15$ years, what should be the sum invested each year for $15$ years at the same interest rate?

Calculate showing formula and detailed working. Amounts may be rounded off to nearest rupee.