Compounding frequency, time value, and effective annual rates For each of the cases in the following table, а. Calculate the future value at the end of the specified deposit period. b. EAR. Determine the effective annual rate, C. Compare the nominal annual rate, r, to the effective annual rate, EAR. What relationship exists between compounding frequency and the nominal and effective annual rates? Case Initial Nom annual rate Comp.frq. Deposit Period A $2,700 7% 25 B $50,000 12% 4 3 C $1,100 7% 1 11 D $20,000 17% 4 8
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- Compare the stated annual rate (r) to the effective annual rate (EAR). What relationship exists between compounding frequency and the stated and effective annual rates? Amount of Compounding Initial Stated Annual Frequency, m Deposit Case Deposit ($) Rate, r (%) (times/year) Period (years) A 2,500 6 2 5 B 50,000 12 6 3 C 1,000 5 1 10 D 20,000 16 4 6Parts a–c for each of the following cases. Answer parts a–c for each of the following cases. Case Amount of Initial Deposit ($) Stated Annual Rate, r(%) Compounding Frequency, m (times/year) Deposit Period (years) A 2,500 6 2 5 B 50,000 12 6 3 C 1,000 5 1 10 D 20,000 16 4 6 a. Calculate the future value at the end of the specified deposit period.b. Determine the effective annual rate (EAR).c. Compare the stated annual rate (r) to the effective annual rate(EAR). What relationship exists between compounding frequency and the stated and effective annual rates?Consider the following cases: Amount of Compounding Initial Stated Annual Frequency, m Deposit Case Deposit ($) Rate, r (%) (times/year) Period (years) A 2,500 6 2 5 B 50,000 12 6 3 C 1,000 5 1 10 D 20,000 16 4 6 a. Calculate the future value at the end of the specified deposit period.
- Method A assumes simple interest over nal fractional periods, while Method B assumes simple discount over nal fractional periods. The annual eective rate of interest is 20%. Find the ratio of the present value of a payment to be made in 1.5 years computed under method A to that computed under Method Bn the credit account statement below, the values of the annual percentage rate (APR), finance charge, and the new balance must be calculated. PreviousBalance AnnualPercentageRate (APR) MonthlyPeriodicRate(as a %) FinanceCharge(in $) Purchasesand CashAdvances PaymentsandCredits NewBalance(in $) $1,026.61 1.75% $322.20 $300.00 Recall that the annual percentage rate (APR) is tied to the monthly periodic rate by the following formula. monthly periodic rate = APR 12 By solving this equation for the APR, the known value for the monthly periodic rate can be substituted to calculate the APR. APR = monthly periodic rate ✕ 12 The monthly periodic rate is given to be 1.75%. Find the APR. APR = 12 ✕ monthly periodic rate = 12 ✕ ____ % = ____%For each of the following cases, indicate (a) to what interest rate columns and (b) to what number of periods you would refer in looking up the future value factor. (Round percentages to 2 decimal places, e.g. 5,275.)(1) In Table 1 (future value of 1): Annual Rate Number ofYears Invested Compounded Case A 4% 3 Annually Case B 9% 5 Semiannually (a) (b) Case A % periods Case B % periods (2) In Table 2 (future value of an annuity of 1): Annual Rate Number ofYears Invested Compounded Case A 6% 5 Annually Case B 12% 6 Semiannually (a) (b) Case A % periods Case B % periods
- For ethe case shown in the following table, determine the amount of the equal, end of year deposits necessary to accumulate the given sum at the end of the specified period, assuming the stated annual interest rate. Sum to be accumulated: $130,000 Accumulation Period (years): 30 Interest Rate: 13% The amount of the end of year annual deposit is? (round to the nearest cent)For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor. 1. In a future value of 1 table: Annual Rate Number ofYears Invested Compounded a. 9% 9 Annually b. 12% 5 Quarterly c. 10% 15 Semiannually 2. In a present value of an annuity of 1 table: Annual Rate Number ofYears Involved Number ofRents Involved Frequency of Rents a. 9% 25 25 Annually b. 10% 15 30 Semiannually c. 12% 7 28 QuarterlyFor the case shown in the following table, determine the amount of the equal, end of year deposits necesssary to accumulate the given sum at the end of teh specified period, assuming the stated annual interest rate. Sum to be accumulated Accumulation Period (Years) Interest Rate $124,600 20 11%
- For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor.1. In a future value of 1 table: Annual Rate Number of Years Invested Compounded (a) Rate of Interest (b) Number of Periods a. 11% 10 Annually % b. 8% 8 Quarterly % c. 10% 19 Semiannually % 2. In a present value of an annuity of 1 table: (Round answers to 1 decimal place, e.g. 458,58.1.) Annual Rate Number of Years Invested Number of Rents Involved Frequency of Rents (a) Rate of Interest (b) Number of Periods a. 12% 30 30 Annually % b. 11% 16 32 Semiannually % c. 12% 8 32 Quarterly %For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i = n = 1. ? $2,400 8% 5 2. 533,082 140,000 ? 4 3. 583,150 180,000 9% ? 4. 530,000 75,502 ? 8 5. 235,000 ? 10% 4For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i=interest rate, and n=number of years)(FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of 1$ and PVAD of $1) (Use appropriate factor (s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i= n= ______________ $ 2,600 8% 5 507,866 135,000 _____ 4 661,241 170,000 9% ____ 540,000 78,557 _____ 8 230,000 _____________ 10% 4