(a) An annuity immediate has semiannual payments of P 10,000 for 10 years at a rate of 6% convert- ible quarterly. Find its present value. (b) An annuity immediate has quarterly payments of P 5,000 for 6 years at a rate of 4% convertible semiannually. Find its present value.
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- (1) What is the value at the end of Year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually? (2) What is the PV of the same stream? (3) Is the stream an annuity? (4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual compounding, when INOM = EFF% = IPER.) What would be wrong with your answers to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate, INOM/2 = 10%/2 = 5%?Define the stated (quoted) or nominal rate INOM as well as the periodic rate IPER. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually—holding the stated interest rate constant? Why? What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?If Bergen Air Systems takes out a $100,000 loan, with eight equal principal payments due over the next eight years, how much will be accounted for as a current portion of a noncurrent note payable each year?
- (b) An annuity immediate has quarterly payments of P 5,000 for 6 years at a rate of 4% convertible semiannually. Find its present value.An annuity immediate has semiannual payments of P 10,000 for 10 years at a rate of 6% convertible quarterly. Find its present value.SHOW MANUAL SOLUTIONSGiven the following situations. Illustrate and distinguish whether it is a simple annuity or a general annuity. 1. Monthly payments of P3,000 for 4 years with an interest rate of 3% Flag compounded monthly 2. Semi-annual payments of P150,000 with an interest rate of 8% compounded rest annually for 10 years. 3. Annual payments of P20.500 with an interest rate of 8.5% compounded semi-annually for 3 years 4. Quarterly payment of P5,000 for 10 years with an interest rate of 2% and compounded quarterly. 5. Quarterly payment of P15.000 for 10 years with an interest rate of 8% compounded annually.
- What is the equivalent present value of the following series of payments: ₱ 5,000 the first year, ₱ 5,500 the second year, and ₱ 6,000 the third year? The interest rate is 8%, compounded annually. a. ₱ 15,904.22 b. ₱ 13,590.43 c. ₱ 12,573.90 d. ₱ 14,107.99Using the appropriate PV table, compute the present value of the following amounts: a. $24,000 payable at the end of each year for 5 years with 12% interest compounded annually.b. $16,000 receivable at the beginning of each semiannual period for 20 years with 10% interest compounded semiannually.c. $3,000 payable at the beginning of the seventh, eighth, and ninth years at 3% compounded annually.Suppose you deposit $2,000 at the end of eachquarter for ten years at an interest rate of 9% compounded monthly. What equal end-of-year depositover the ten years would accumulate the same amountat the end of the ten years under the same interestcompounding? To answer the question, which of thefollowing is correct?(a) A = $2,000(F/A, 2.267%, 4)(b) A = $2,000(F/A, 9%12 , 40) * (A/F, 9%, 10)(c) A = [$2,000(F/A, 2.25%, 40)] * (A/F, 9%, 10)(d) None of the above
- Assume the following annual payments of notes payable of Demi Company with 10% discount rate. 1st Year - P300,0002nd Year - P200,000 3rd Year - P400,000 What is the present value of the annual payments?(a) Find the nominal rate per annum convertible quarterly that makes an interest payment of £150 on an initial capital of £1,000, at the end of 2 years. (b) Find the annual effective rate of discount equivalent to a nominal interest rate of 2% p.a. convertible semi-annually.(a) Compute the present value of an annuity immediate that pays £50 per year for 10 years at an effective rate of 7% p.a. (b) Compute the accumulated value after 10 years of an annuity immediate that makes quarterly payments of £50 at an effective rate of 3% p.a.