Re: Please assist me with this problem on Annuity.
The fact that it's an 'annuity due' (with the initial 10K cash flow occurring immediately) can be dealt with as follows. Not the only way, but it's pretty straightforward.
To answer the first question, the purchaser gives you 60,000 but immediately gets back 10K from the annuity. In effect, the seller is out 50K up front, but then owns 9 inflows of 10K each, beginning one year from now. Treat this, then, as the purchase of a 9-payment ordinary annuity for 50,000. So set up 10 cash flows in Excel, the first being -50,000 followed by 9 at +10,000 each. Hit that stack of numbers with Excel's IRR function and you're done.
For the second question, just use the spreadsheet's NPV function to determine the present value of 9 cash flows of 10K each, at a 6% discount rate. Disregarding the first cash flow for a moment, this would be the price you'd charge the purchaser to sell her cash flows numbers 2 through 10 (i.e., a 9-payment ordinary annuity). Then simply add $10K to that total price, since you'd obviously charge her $10,000 to sell her the first cash flow, given that it occurs immediately.