Find the value of the required components in each item. 1. Find the compound interest and maturity value if P = P43,000, with a rate of 5% is compounded semi-annually for 6 years. 2. Find the compound interest and present value if F = P105,000 with a rate of 2.5% is compounded quarterly for 3 years %3! Activity 2.3 Complete the table below by finding the unknown. Compound Maturity Value Present Nominal Interest Interest Time Total Value rate (ilm) compounded per in number of Interest conversion years conversions period (j) (n) 50,000 3% quarterly 6% semi- 4 40,000 annually

Find the value of the required components in each item. 1. Find the compound interest and maturity value if P = P43,000, with a rate of 5% is compounded semi-annually for 6 years. 2. Find the compound interest and present value if F = P105,000 with a rate of 2.5% is compounded quarterly for 3 years %3! Activity 2.3 Complete the table below by finding the unknown. Compound Maturity Value Present Nominal Interest Interest Time Total Value rate (ilm) compounded per in number of Interest conversion years conversions period (j) (n) 50,000 3% quarterly 6% semi- 4 40,000 annually

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose a principal P is invested at the annual (nominal) rate 7 compounded m times a year for t years. Check all of the terms below that describe the quantity (1+) - 1. m annual percentage yield amount present value future value effective rate nominal rate principal true interest rate interest rate annual rate
Complete the following using compound future value. (Use the Table 12.1 provided.) Note: Round your answers to the nearest cent. Time: 12 years Principal: $17,300 Rate: 3% Compounded: Annually Amount: Interest: Future value interest factor of $1 per period at i% for n periods, FVIF(i,n). Period 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 1 1.0050 1.0100 1.0150 1.0200 1.0250 1.0300 1.0350 1.0400 1.0450 1.0500 1.0550 1.0600 1.0650 1.0700 1.0750 1.0800 1.0850 1.0900 1.0950 1.1000 2 1.0100 1.0201 1.0302 1.0404 1.0506 1.0609 1.0712 1.0816 1.0920 1.1025 1.1130 1.1236 1.1342 1.1449 1.1556 1.1664 1.1772 1.1881 1.1990 1.2100 3 1.0151 1.0303 1.0457 1.0612 1.0769 1.0927 1.1087 1.1249 1.1412 1.1576 1.1742 1.1910 1.2079 1.2250 1.2423 1.25.97 1.2773 1.2950 1.3129 1.3310 4 1.0202 1.0406 1.0614 1.0824 1.1038 1.1255 1.1475 1.1699 1.1925 1.2155 1.2388 1.2625 1.2865 1.3108 1.3355 1.3605 1.3859 1.4116 1.4377 1.4641 5 1.0253…
Calculate the present value of the following annulties, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of S1) (Use tables, Excel, or a financial calculator. Round your answers to 2 decimal places.) \table[[, \table[[Annuity], [Payment]], \table [[ Annual], [Rate]], \table[[Interest], [Compounded]], \table [[Period], [Invested]], \table [[Present Value of], [ Annuity]]], [1., $5,000, 7.0%, Semiannually,3 years,], [2., 10, 000, 8.0%, Quarterly,2 years, ], [3., 4,000, 10.0 %, Annually,5 years,]]
4. Non annual compounding period The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows. An investor can invest money with a particular bank and earn a stated interest rate of 11.00%; however, interest will be compounded quarterly. Complete the following table by computing the nominal (or stated), periodic, and effective interest rates for this investment opportunity. Interest Rates Nominal rate : Periodic rate Effective annual rate Clancy needs a loan and is speaking to several lending agencies about their interest rates and loan terms. He particularly likes his local bank because he is being offered a nominal rate of 10.00%. However, since the bank is compounding its interest semiannually, the loan will impose an effective interest rate of on his loan. Another bank is also offering favorable terms, so Clancy decides to take a loan of $15,000 from this bank. He signs the loan…
Assume that at time 0 a sum L is lent for a series of n yearly payments. The rth payment, of amount xr, is due at the end of the rth year. Let the effective annual interest rate for the rth year be ir. Give an identity which expresses L in terms of the xr and ir.
Derive an equation to find the end-of-year future sum F that is equivalent to a series of n beginning-of-year payments B at interest rate i. Then use the equation to determine the future sum F equivalent to six B payments of $100 at 8% interest.
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 a. 9% 12 Annually b. 8% 7 Quarterly C. 12% 16 Semiannually % % % (b) Number of Periods 2. In a present value of an annuity of 1 table: (Round "Rate of Interest" answers to 1 decimal place, e.g. 4.5% and other answers to O decimal places, e.g 45.) Annual Number of Years Rate Invested Number of Rents Involved Frequency of Rents (a) Rate of Interest (b) Number of Periods a. 10% 28 28 Annually b. 10% 15 30 Semiannually % % 8% 7 28 Quarterly %
The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(rt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?
For each of the following cases, indicate (a) what interest rate columns and (b) what number of periods you would refer to in looking up the future value factor. (1) In Table 1 (future value of 1): Number of Annual Rate Years Invested Compounded Case A 5% 5 Annually Case B 8% 6 Semiannually Case A Case B . (a) % % (2) In Table 2 (future value of an annuity of 1): Annual Rate Number of Years Invested Compounded Case A 6% 9 Annually Case B 8% 5 Semiannually Case A Case B (b) periods periods (a) (b) % periods % periods
Consider a future value of $2,000, 8 years in the future. Assume that the nominal interest rate is 18.00%. Assume that there is semiannual compounding. Entering PMT=0 and a FV=$2,000 into a financial calculator, along with the appropriate periodic interest rate and value of N, yields a present value of approximately $ with semiannual compounding. Assume that there is quarterly compounding. Entering PMT=0 and a FV=$2,000 into a financial calculator, along with the appropriate periodic interest rate and value of N, yields a present value of approximately $ with quarterly compounding. Suppose now that the cash flow of $2,000 occurs only 1 year in the future. Assume that there is monthly compounding. Entering PMT=0 and a FV=$2,000 into a financial calculator, along with the appropriate periodic interest rate and value of N, yields a present value of approximately $ with monthly compounding.
*Using Matlab* The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(nt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?

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