Apply the concept from page 8-7 “Interest rates and compounding periods,” you have the opportunity to invest $10,000 today and will earn interest every month at the market rate of 9% for the next 4 years. When determining the future value of this investment at the end of four years, you would use __n (compounding periods) and __%.Group of answer choicesA. 0.33n and 108%B. 4n and 9%C. 48n and 0.75%D. 8n and 4.5% APPENDIX C, TIME VALUE OF MONEY (“TVM") (end oftext, pages C-1 to C-13)"A dollar today is worth more than a dollar in the future."Assumptions:1. The dollar is invested today2. The dollar is earning a positive return» 41+ interestFV $1Simple interest: P x R x TCompound interest-Compounding (Future Value “FV")-Discounting (Present Value "PV"). In Accounting we recordlong term assets and long-term liabilities at their present value(cash equivalent amount); therefore, we mostly use PRESENTVALUE concepts.Two types of CASH FLOWSANNUITY–very specific–it is the same dollar amount thatoccurs the same time each period.SINGLE SUM– A single sum can occur at any time at anyamount. It is possible to have multiple single sum cash flows inan investment; an amount that does not occur at the same timeeach period.A cash flow is either an annuity OR a single sum, it cannotbe both.Ordinary Annuity (Payment = $50)$50 $50 $50 $50 $50 $50 $50 $50 $50 $501 2 3 4 5 6 7 8 9 10Single sum (example of 2 single sums, $500 and $1,000)$500$1,00012345678910An investment with two types of cash flows (annuity ($50payment) and a $1,000 single sum)$1,000$50 $50 $50 $50 $50 $50 $50 $50 $50 $501 2 3 4 5 6 7 8 9 10 PV and FV Tables (available in Camvas) or use the BAII Plus Financial Calculator)Future Value of a Single Amount (FV$1) Factor = (1+j"Where (is the interest rate and n is the number of compounding periods.Present Value of a Single Amount (PV$1) Factor= 1/(1+j the PV$1 Is the reciprocal of the FV$1Future Value of an Ordinary Annulty (FVA) Factor= (FV$1-1)/1Present Value of an Ordinary Annuity (PVA) Factor=1-PV$1)/1Interest rates are stated in annual terms (one year, 12 months, 365 days...sometimes 360 days)If compounding occurs more than once a year, the interest rate į needs to be divided (RxT) toreflect the number of compounding periods in a year. And "n" needs to reflect the total numberof compounding periods over the life of the investment. For example:An investment pays 12% interest annually for 5 years:An investment pays 12% interest semiannually for 5 years: (6%, 10n) interest is cut in half,(12%, 5n)compounding periods are doubled.(3%, 20n) interest is cut in fourth,compounding periods are quadrupled.(1%, 60n) interest is cut in 12ths,compounding periods multiplied by 12.An investment pays 12% interest quarterly for 5 years:An investment pays 12% interest monthly for 5 years:IDENTIFY (4 of the 5 variables, solve for the 5th):number of compounding periods over the life of the investment/borrowinginterest rate (affected by compounding periods) earned on investmenta single sum (the amount today)an annuity (equal cash flows that occur at the same time each period)a single sum (the amount in the future)PVPMTFVUsing the factor tables the equation to use is:Cash flow x factor = VALUEWhere:Cash flow is either a single sum (PV or FV) or the payment (PMT)Factor is based on the %, n, single sum or annuity, PV or FVValue is dependent on the factor (PV or FV) usedIf a present value FACTOR is used, the VALUE will be the present value. If a future valueFACTOR is used, the VALUE will be the Future value.For BAII Plus Financial Calculator:Set P/Y to 1 by pressing the 2ND key and then the (1/Y) key. Type in 1 and press enter. Thenpress the 2ND key and then the CPT key.Following are the keys to use for Time Value of Money on the BAlIl Plus Financial CalculatorN= number of compounding periodsI/Y = interest ratePV = present valueTo quit/clear, press 2ND then CPT and then 2ND then FV. (Note: turning off the calculator willnot clear the TVM items).PMT = annuity cash flow (payment)FV = Future ValueCPT = compute keyChanter 8Page 8-7

Question

Apply the concept from page 8-7 “Interest rates and compounding periods,” you have the opportunity to invest $10,000 today and will earn interest every month at the market rate of 9% for the next 4 years.  When determining the future value of this investment at the end of four years, you would use __n (compounding periods) and __%.Group of answer choicesA. 0.33n and 108%B. 4n and 9%C. 48n and 0.75%D. 8n and 4.5% APPENDIX C, TIME VALUE OF MONEY (“TVM&#34;) (end oftext, pages C-1 to C-13)&#34;A dollar today is worth more than a dollar in the future.&#34;Assumptions:1. The dollar is invested today2. The dollar is earning a positive return» 41+ interestFV $1Simple interest: P x R x TCompound interest-Compounding (Future Value “FV&#34;)-Discounting (Present Value &#34;PV&#34;). In Accounting we recordlong term assets and long-term liabilities at their present value(cash equivalent amount); therefore, we mostly use PRESENTVALUE concepts.Two types of CASH FLOWSANNUITY–very specific–it is the same dollar amount thatoccurs the same time each period.SINGLE SUM– A single sum can occur at any time at anyamount. It is possible to have multiple single sum cash flows inan investment; an amount that does not occur at the same timeeach period.A cash flow is either an annuity OR a single sum, it cannotbe both.Ordinary Annuity (Payment = $50)$50 $50 $50 $50 $50 $50 $50 $50 $50 $501 2 3 4 5 6 7 8 9 10Single sum (example of 2 single sums, $500 and $1,000)$500$1,00012345678910An investment with two types of cash flows (annuity ($50payment) and a $1,000 single sum)$1,000$50 $50 $50 $50 $50 $50 $50 $50 $50 $501 2 3 4 5 6 7 8 9 10 PV and FV Tables (available in Camvas) or use the BAII Plus Financial Calculator)Future Value of a Single Amount (FV$1) Factor = (1+j&#34;Where (is the interest rate and n is the number of compounding periods.Present Value of a Single Amount (PV$1) Factor= 1/(1+j the PV$1 Is the reciprocal of the FV$1Future Value of an Ordinary Annulty (FVA) Factor= (FV$1-1)/1Present Value of an Ordinary Annuity (PVA) Factor=1-PV$1)/1Interest rates are stated in annual terms (one year, 12 months, 365 days...sometimes 360 days)If compounding occurs more than once a year, the interest rate į needs to be divided (RxT) toreflect the number of compounding periods in a year. And &#34;n&#34; needs to reflect the total numberof compounding periods over the life of the investment. For example:An investment pays 12% interest annually for 5 years:An investment pays 12% interest semiannually for 5 years: (6%, 10n) interest is cut in half,(12%, 5n)compounding periods are doubled.(3%, 20n) interest is cut in fourth,compounding periods are quadrupled.(1%, 60n) interest is cut in 12ths,compounding periods multiplied by 12.An investment pays 12% interest quarterly for 5 years:An investment pays 12% interest monthly for 5 years:IDENTIFY (4 of the 5 variables, solve for the 5th):number of compounding periods over the life of the investment/borrowinginterest rate (affected by compounding periods) earned on investmenta single sum (the amount today)an annuity (equal cash flows that occur at the same time each period)a single sum (the amount in the future)PVPMTFVUsing the factor tables the equation to use is:Cash flow x factor = VALUEWhere:Cash flow is either a single sum (PV or FV) or the payment (PMT)Factor is based on the %, n, single sum or annuity, PV or FVValue is dependent on the factor (PV or FV) usedIf a present value FACTOR is used, the VALUE will be the present value. If a future valueFACTOR is used, the VALUE will be the Future value.For BAII Plus Financial Calculator:Set P/Y to 1 by pressing the 2ND key and then the (1/Y) key. Type in 1 and press enter. Thenpress the 2ND key and then the CPT key.Following are the keys to use for Time Value of Money on the BAlIl Plus Financial CalculatorN= number of compounding periodsI/Y = interest ratePV = present valueTo quit/clear, press 2ND then CPT and then 2ND then FV. (Note: turning off the calculator willnot clear the TVM items).PMT = annuity cash flow (payment)FV = Future ValueCPT = compute keyChanter 8Page 8-7

Accepted Answer

Future Value = Present Value x (1 + r)^n
Compounding Frequency = monthly