# TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007

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1 TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007 The purpose of this tutorial is to help students who use the HP 17BII+, and HP10bll+ calculators understand how to perform the calculations discussed in the TVM Math Formula handout. Note that the key words, to help you understand whether it is present value, future value, or an annuity, are italicized, underlined, and it bold face. 1. Future Value (FVIF) This is the value of an investment at some point in the future, used for planning and forecasting purposes. A possible question would be: I have \$2,500 saved. If my investment earns 10% per year for 20 years, how much will it be worth in 20 years (this indicates future value)? The math formula is: FV = PV (1 + i) n where FV = future value, PV = present value, i=interest rate, n = number of years or FV = \$2,500 * (1 +.10) 20 or \$16, ALL] to clear the memories. Then press 1 orange [[o]][p/yr] [[o]][c ALL] to change the payments to annual payments and [[o]][beg/end to set your payments for the end of the period. If it is in BEGIN mode, you will see a BEGIN in the lower bottom display. The problem then is 2500 [+/-][PV], 10 [I/YR], 20 [N], and then [FV] for the Note that the 12C has two [2 nd ] keys, the orange [[o]] key and blue [[b]] key. Type [[o]][clear FIN] to clear the financial registers and [[o]][clear REG] to clear the registers. Then press [[b]] [END] set your payments for the end of the period. The problem then is 2500 [CHS][PV], 10 [i], 20 [n], and then [FV] for the First press [EXIT][EXIT] to return to the basic mode. Note that the [2 nd ] or [[o]] key is the orange key just above the OFF button. Type [[o]][clear DATA] to clear the memories. Then press [FIN][TVM] to go to the TVM menu. Then press [OTHER] 1 [P/YR] [EXIT] to change the payments to annual payments and [OTHER] [END] [EXIT] to set your payments for the end of the period. The problem then is 2500 [+/-][PV], 10 [I%YR], 20 [N], and then [FV] for the 2. Present Value (PVIF) This is the current value, that is, the value in today s dollars, of a future sum of money or stream of money. A possible question would be: I am planning to have \$500,000 saved by the time I turn 65, which is 40 years from now. Assuming I can make 6% on my money, what is the value of that money now (this indicates present value)? The math formula is: PV = FV/ (1 + i) n Note that this is just the re-arrangement of terms from the above Future Value formula. Starting with the above FV formula, FV = PV (1 + i) n, you multiply each side by 1/(1 + i) n to get: FV/ (1 + i) n = PV or the PV = FV/ (1 + i) n or PV = 500,000/ (1.06) 40 or \$48, Page 1 of 5 -

2 ALL] to clear the memories. The problem then is 500,000 [+/-][FV], 6 [I/YR], 40 [N], and then Type [[o]][clear FIN] to clear the financial registers and [o]][clear REG] to clear the is 500,000 [CHS][FV], 6 [i], 40 [n], and then First press [EXIT][EXIT] to return to the basic mode. Type [[o]][clear DATA] to clear the memories. Then press [FIN][TVM] to go to the TVM menu. Then press [OTHER] 1 [P/YR] [EXIT] to change the payments to annual payments. The problem then is 500,000 [+/-][FV], 6 [I%YR], 40 [N], and then 3. FVIF of an Annuity A multiplier used to determine the future value of an annuity or future value of a set of constant payments. This is used to answer the question: Assuming I make a \$2,500 payment every year (this is an annuity) for 30 years, and given the discount or interest rate is 5%, what will be the value of my investment when I retire in 30 years (this is future value)? The math formula is a bit more tricky. The formula is FV n = Payment * (FVIFA i,n ) or FV n,i = Payment * [(1 + i) n -1] /i = FV = \$2,500 * [(1.05) 30-1]/.05 = \$166, is 2,500 [CHS][PMT], 5 [i], 30 [n], and then [FV] for the ALL] to clear the memories. The problem then is 2500 [+/-][PMT], 5 [I/YR], 30 [N], and then [FV] for the Type [[o]][clear DATA] to clear the memories. Then press [FIN][TVM] if you are not already in the TVM menu. Then press [OTHER] 1 [P/YR] [EXIT] to change the payments to annual payments. The problem then is 2500 [+/-][PMT], 5 [I%YR], 30 [N], and then [FV] for the 4. PVIF of an Annuity A multiplier used to determine the present value of an annuity or constant periodic payments. To compare annuities, you need to put them all on a constant basis and compare the present value, in today s dollars, of each. This factor is used to answer a possible question such as: Assuming I will make \$2,000 payments every year (this is an annuity) for 40 years into an IRA account, and given the discount or interest rate is 6%, what is the current value (that is the present value) of my investment in today s dollars? The formula is PV n,i = Payment * (PVIFA n,i ) or PV n,i = Payment * [ 1-( 1/(1 + i) n )]/i = PV = 2,000 * [1-(1/(1.06) 40 ] /.06 = \$30, Page 2 of 5 -

3 ALL] to clear the memories. The problem then is 2000 [+/-][PMT], 6 [I/YR], 40 [N], and then is 2,000 [CHS][PMT], 6 [i], 40 [n], and then menu if you are not already there. Then press [OTHER] 1 [P/YR] [EXIT] to change the payments to annual payments. The problem then is 2000 [+/-][PMT], 6 [I%YR], 40 [N], and then 5. Amortized Loan A loan paid off in equal installments, both principle and interest is an amortized loan. It is similar to an annuity. It is used to answer the possible question: Assuming you want to borrow \$20,000 dollars at 13% interest and you want to repay it in 5 annual payments (this is an annuity), how much will you have to pay each year (this indicates present value)? The formula is the same as that shown above, i.e. PV n = Payment * (PVIFA i,n ). Put your borrowed amount into the equation, and solve for your payment. PV n,i = Payment * [ 1-( 1/(1 + i) n )]/i = PV = 20,000 = Payment * [1-(1/(1.13) 5 ] /.13 = \$5, per year. ALL] to clear the memories. The problem then is 20,000 [+/-][PV], 13 [I/YR], 5 [N], and then [PMT] for the is 20,000 [CHS][PV], 13 [i], 5 [n], and then [PMT] for the menu if you are not already there. Then press [OTHER] 1 [P/YR] [EXIT] to change the payments to annual payments. The problem then is 20,000 [+/-][PV], 13 [I%YR], 5 [N], and then [PMT] for the. Now the question is: What happens if instead of solving for annual payments, we want to solve for monthly payments. Below is the process for solving the above problem for monthly versus annual payments (the answer is \$455.06) - Page 3 of 5 -

4 Type [[o]][c ALL] to clear the memories. Then press 12 [[o]][p/yr] [[o]][c ALL] to change the payments to monthly payments and [[o]][beg/end to set your payments for the end of the period. The problem then is 20,000 [+/-][PV], 13 [I%YR], 5 [[o]] [N], and then [PMT] for the is 20,000 [CHS][PV], 13 [[b]] [i], 5 [[b]] [n], and then [PMT] for the menu if you are not already there. Then press [OTHER] 12 [P/YR] [EXIT] to change the payments to monthly payments. The problem then is 20,000 [+/-][PV], 13 [I%YR], 5 [[o]] [N], and then [PMT] for the Key Formulas for Personal Finance 1. Future Value (FVIF) The value of an investment at some point in the future, used for planning and forecasting purposes. The question would be: I have \$2,500 saved. If my investment earns 10% per year for 20 years, how much will it be worth in 20 years? The math formula is: FV = PV (1 + i) n where FV = future value, PV = present value, i=interest rate, n = number of years FV = \$2,500 * (1 +.10) 20 or \$16, This is the same formula for compounding, except with a minor difference. The formula for compounding is FV = PV (1 + i/p) np The i is the annual interest rate but divided by p, the period for compounding. The exponent is the number of years n times the number of periods for compounding p. 2. Present Value (PVIF) The current value, that is, the value in today s dollars, of a future sum of money or stream of money. A possible question would be: I am planning to have \$500,000 saved by the time I turn 65, which is 40 years from now. Assuming I can make 6% on my money, what is the value of that money now? The math formula is: PV = FV/ (1 + i) n Note that this is just the re-arrangement of terms from the above formula. Starting with the above FV formula, FV = PV (1 + i) n, you multiply each side by 1/(1 + i) n to get: FV/ (1 + i) n = PV or the PV = FV/ (1 + i) n PV = 500,000/ (1.06) 40 or \$48, Page 4 of 5 -

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