FUTURE VALUE SINGLE LUMP SUM PAYMENT Practice Problem 1.1 Compounding lnterest Future Value [FV] You deposit $1,000 today.' with ABC Bank. The bank will give .03 percent interest. How much you will receive at the end of 10 [ten] years ? N :10, r2118, pvIDOO 1What is r? Answer $2,158.93 Practice Problem 1.2. Practice Problem H! Com pounded Interest - Compute Hr [Future Value} pv {present value) :1 {number of period}- Yea: r (fuhilre vine _ in eras m R {rate of Compute fv interest} {future value} 0.05 PRESENT VALUE - SINGLE LUMP SUM PAYMENT Practice Problem 2.1. Practice Problem PV Compounded Interest - Compute PV (Present Value) fv (future In (number of period) - |R (rate of pv (present Year value - value) interest) (ANSWER) $1,000 0.07 2. $1,000 0.09 Compute Problem 2.2 - Compute PV ( Value) - Compunding Interest FV(Future n (number of period) - R (rate of Compute pv Value) Year interest) (present value) 1000 2 0.05 IN P 1000 6 0.03 3 1000 7 0.04 Practice Problem 3.1 - r (interest rate) Solving for Interest Rate Problem 3.1. Finding Interest Rate Assume that the present value of an investment is $1,000, the future value is $1,403, the time period is 5(Five) years. What is the compound rate of interest for the investment N =5, pv - $1,000, fv $1,403, what is r= ? AnswerPractice Problem 3.2 - r (interest rate) Compute Interest Rate fv (future value) |n (number of period) - Year pv (present r (interst rate - value (ANSWER) $1.000 9 -766.14 $1,000 -747.258 3 $1.000 -710.681 Compute Problem 3.3 - r (interest rate) Compute Interest Rate fv (future value) n (number of period) - Year pv (present r (interst rate - value (ANSWER) $1.000 9 -766.14 $1,000 -747.258 3 $1.000 -710.681 Practice Problem 4.1 - n (number of period) Solving fornumber of period Practice Problem 4.2. Finding n number of period Assume that the present value of an investment is -$1,000, the future value is $1,403, the interest rate is .07. What is the time period ? r =.07, pv - $1,000, fv $1,403, what is n = ? AnswerPractice Problem 4.3 - n (number of periods) Compute number of periods fv (future pv (present n (number of value) r (interest rate) periods - value) (ANSWER) $1.000 0.03 -766.14 2 $1,000 0.06 -747.258 3 $1.000 0.05 -710.681 Compute Problem 4.4 - n (number of periods) Compute number of periods fv (future pv (present n (number of value) r (interest rate) value) period) - Year ANSWER $1.000 0.09 -755.14 2 $1,000 0.05 -737.258 3 $1.000 0.04 -720.681 ANNUITY - MULTIPLE PAYMENTS MADE OR RECEIVED FUTURE VALUE [FV) For ANNUITYProblem 5. 1. Annuity - Multiple Payments - Compounding Interest - Annuity - Future Value (FV) You deposit $0 now, $1,000 at the end of year 1, $1,000 at the end of year 2, and $1,000 at the end of year 3 with ABC Bank. The bank will give .08 percent interest. How much you will receive at the end of 3 (three) years ? N = 3, r=.08, PMT - 1000 end of yr 1, at the end of year 2, - 1000 end of yr 3. Compute the FV. ANSWER Problem 5. 2. Annuity - Multiple Payments - Compounding Interest - Annuity - Compute Future Value (FV) PMT n (number fv (future (Payments) r(rate of interest) of period) - value) Year ANSWER 1 -1000 0.03 9 -1000 0.06 -1000 0.05 7 Problem 5. 3. Annuity - Multiple Payments - Compounding Interest - Annuity - Compute Future Value (FV) PMT n (number fv (future (Payments) r(rate of interest) of period) value) Year ANSWER 1 -1000 0.03 9 N -1000 0.06 -1000 0.08 7PRESENT VALUE [FV) For ANNUITY Problem 6.1. Multiple Payments - Compounding Interest - Annuity - Present Value (PV) You will receive $1,000 per year beginning one year from now for a period of 3(three) years at an 8 percent interest rate. How much will you be willing to pay now for this stream of cash flow ? N = 3, r=.08, PMT 1000 to be received end of yr 1, 2,3. Compute the PV of the money you are willing to pay. Answer 6.2. Practice Problem - - Annuity - Compute Present Value PMT n (number pv (present (Payments) r(rate of interest) of period) - Year value) 1000 0.03 9 2 1000 0.06 5 3 1000 0.05 7 6.3. Compute Problem - -Annuity - Compute Present Value PMT n (number pv (present (Payments) r(rate of interest) of period) - Year value) 1000 0.03 9 1000 0.06 5 1000 0.04 7Practice Problem 11. FINDING ANNUAL Annuil_.y_ PAYMENTS It is necessary in many instances to determine the periodic equal payments required for an annuity. For example, you like to accumulate $10,000 at the end of 5 {ve} years from now by making equal annual payments beginning one year from now. lfyou can invest at a compound 6% [Six percent} interest rate, what will be the amount of each ofyour annual payments