1. Compare the final amounts at the end of a year of$100 invested at 5% in two ways: simple interest andcontinuous compound interest.2. A radioactive substance is known to have a half-life of78 years. Calculate the number of years it would takefor this substance to decrease to 10% its originalamount.3. A city has been found to have a population that triplesevery four years. If the city's population is one millionin 2010, how many people were there in 1990?

Note: Since more than one question is posted. I Provide a solution to question number 1. Kindly…

Answered: 1. Compare the final amounts at the end…

1. Compare the final amounts at the end of a year of $100 invested at 5% in two ways: simple interest and continuous compound interest.

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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Concept explainers

Present Value

Present value (PV) is defined as the current or present value of all future sums of cash flow or money at a specified rate of return. This rate of return is known as the discounted rate, which is essentially the interest rate, discounted over some time. The expected cash flows are discounted at a discount rate to compute the present value. The higher the discount rate, the higher the future value (FV), but the lower the present value.

Question

1. Compare the final amounts at the end of a year of
$100 invested at 5% in two ways: simple interest and
continuous compound interest.
2. A radioactive substance is known to have a half-life of
78 years. Calculate the number of years it would take
for this substance to decrease to 10% its original
amount.
3. A city has been found to have a population that triples
every four years. If the city's population is one million
in 2010, how many people were there in 1990?

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Using Table 11-1, compute the amount of compound interest (in $) earned in 1 year and the annual percentage yield (APY) for the investment. (Round your answers to two decimal places.) Principal NominalRate (%) InterestCompounded Compound InterestEarned in 1 Year Annual PercentageYield (APY) $6,000 12 semiannually $ %
Using Table 11-2 from your text, calculate the present value (principal) and the compound interest given: A = Compound Amount = $1,250 t = Term of Investment = 6 years r = Nominal rate = 6% or 0.06 n = Interest is compounded semiannually = 2
Using Table 11-1, compute the amount of compound interest (in $) earned in 1 year and the annual percentage yield (APY) for the investment. (Round your answers to two decimal places.) Compound Interest Earned in 1 Year Annual Percentage Yield (APY) Nominal Interest Principal Rate (%) Compounded $33,000 12 monthly $ % Need Help? Read It 3 Type here to search
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?
Using Table 11-1, calculate the compound amount and compound interest (in $) for the investment. (Round your answers to the nearest cent.) Time Nominal Interest Compound Compound Principal Period (years) Rate (%) Compounded Amount Interest $5,100 8 quarterly Need Help? Read It
*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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Using Table 11-1, calculate the compound amount and compound interest (in $) for the investment. (Round your answers to the nearest cent.) Time Nominal Interest Compound Compound Principal Period (years) Rate (%) Compounded Amount Interest $23,000 13 5 annually Need Help? Read It
Use the continuous compound interest formula to find the indicated value. A= $16,687; P=$10,400; t= 60 months; r= ?
Calculate the simple interest earned. Round to the nearest cent. P = $4700, r = 7%, t = 1 year
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