Time Value of Money
Time Value of Money Practice Problems − Solutions
Dr. Stanley D. Longhofer 1) Jim makes a deposit of $12,000 in a bank account. The deposit is to earn interest annually at the rate of 9 percent for seven years. a) How much will Jim have on deposit at the end of seven years? P/Y = 1, N = 7, I = 9, PV = 12,000, PMT = 0 ⇒ FV = $21,936.47 b) Assuming the deposit earned a 9 percent rate of interest compounded quarterly, how much would he have at the end of seven years? P/Y = 4, N = 7 × 4 = 28 ⇒ FV = $22,374.54 c) In comparing parts (a) and (b), what are the respective effective annual yields? Which alternative is better? Because interest in compounded annual in part (a), the effective annual rate is the same as the nominal rate: EARA = 9%. In part (b), EARB = (1 + i/m)m – 1 = 1.02254 – 1 = 9.31%. This can be also solved using the TI BAII+ using the Interest Conversion worksheet. Simply press [2nd] [I Conv] (the second function of the 2 key) to bring up this worksheet. When the screen says NOM = press [9] and [Enter]. Then arrow up and make sure that [C/Y] reads 4 compounding periods per year; if not, press [4] and [Enter]. Finally arrow up to the EFF screen and press [CPT] to compute the effective annual rate. Alternative (b) is preferred because it compounds your interest more frequently. Thus you get to earn “interest on your interest” sooner. 2) John is considering the purchase of a lot. He can buy the lot today and expects the price to rise to $15,000 at the end of 10 years. He believes that he should earn an investment yield of 10 percent annually on this investment. The asking price for the lot is $7,000. Should he buy it? What is the annual yield (internal rate of return) of the investment if John purchases the property for $7,000 and is able to sell it 10 years later for $15,000? P/Y = 1, N = 10, I = 10, PMT = 0, FV = 15,000 ⇒ PV = − $5,783.15. Because the present value of this investment is less than the $7,000 asking price for the lot, John should not buy it.
Dr. Stanley D. Longhofer 1) Jim makes a deposit of $12,000 in a bank account. The deposit is to earn interest annually at the rate of 9 percent for seven years. a) How much will Jim have on deposit at the end of seven years? P/Y = 1, N = 7, I = 9, PV = 12,000, PMT = 0 ⇒ FV = $21,936.47 b) Assuming the deposit earned a 9 percent rate of interest compounded quarterly, how much would he have at the end of seven years? P/Y = 4, N = 7 × 4 = 28 ⇒ FV = $22,374.54 c) In comparing parts (a) and (b), what are the respective effective annual yields? Which alternative is better? Because interest in compounded annual in part (a), the effective annual rate is the same as the nominal rate: EARA = 9%. In part (b), EARB = (1 + i/m)m – 1 = 1.02254 – 1 = 9.31%. This can be also solved using the TI BAII+ using the Interest Conversion worksheet. Simply press [2nd] [I Conv] (the second function of the 2 key) to bring up this worksheet. When the screen says NOM = press [9] and [Enter]. Then arrow up and make sure that [C/Y] reads 4 compounding periods per year; if not, press [4] and [Enter]. Finally arrow up to the EFF screen and press [CPT] to compute the effective annual rate. Alternative (b) is preferred because it compounds your interest more frequently. Thus you get to earn “interest on your interest” sooner. 2) John is considering the purchase of a lot. He can buy the lot today and expects the price to rise to $15,000 at the end of 10 years. He believes that he should earn an investment yield of 10 percent annually on this investment. The asking price for the lot is $7,000. Should he buy it? What is the annual yield (internal rate of return) of the investment if John purchases the property for $7,000 and is able to sell it 10 years later for $15,000? P/Y = 1, N = 10, I = 10, PMT = 0, FV = 15,000 ⇒ PV = − $5,783.15. Because the present value of this investment is less than the $7,000 asking price for the lot, John should not buy it.