# Solutions to Tvm

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1. James plans to fund his individual retirement account, beginning today, with 20 annual deposits of \$2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be 98845.84(since it is a retirement plan so, assumed to be annuity due) correct 91,523.93 – ordinary annuity in this accumulation phase. 2. \$100 is received at the beginning of year 1, \$200 is received at the beginning of year 2, and \$300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is __727.37____. 3. Marla borrows \$4,500 at 12 percent annually compounded…show more content…
Inflation is expected to cause this price to increase at 5 percent per year over the next 20 years before Luci and Kishore retire from successful careers in commercial art. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the beach house upon retirement? (Time/Marks 3) ANSWER: Value of the house at retirement = FV20 = Rs.92,86,541.97; Annual Saving = Annuity ordinary = Rs.1,14,723.97. Q 5. An oil well presently produces 50,000 barrels per year. It will last for 15 years more, but the production will fall by 5% p.a. Oil prices are expected to increase by 3% p.a. Currently the price of oil is \$50 per barrel. What is the present value of the well’s production if the discount rate is 10% p.a. effective. (Time/Marks 5) ANSWER: 1 + Adjusted interest rate = 1+i = 1.10 /(0.95*1.03) = 1.124169647 => Adjusted interest rate = i = 0. 124169647; So the given cash flow stream (a growing annuity) is equivalent to a level annuity of Rs.25 lakh for 15 years @ an adjusted interest rate of i = 0. 124169647 => So the PVOA15 = (50,0000 x 50) x PVIFOA12.417%,15yrs = \$25,00,0000 x 6.661923 = \$166,54,807/-. Q. 4. Ellen is 35 and decides to plan seriously for her retirement. She wants to save Rs.10,000 in the 1st year, i,e., starting @ age 36. However, she expects her salary to increase each year so that she will be able to increase her savings by 5% per year from 2nd year