You invest B, dollars in an account that draws interest at a monthly rate of r as a decimal, compounded monthly. After t months, the balance in dollars is given by the following. B- B,(1 + r)t (a) Let a denote the APR as a decimal. Then the monthly rate as a decimal is equal to a divided by 12. Express the balance in terms of the initial investment, the number of months, and the APR as a decimal. B(t) - (b) Let a denote the APR as a decimal, and let A denote the APR as a percentage. Then a is equal to A divided by 100. Express the balance in terms of the initial investment, the number of months, and the APR as a percentage. B(t) - (c) Note that y years is equivalent to 12y months. Express the balance in terms of the initial investment, the number y of years, and the APR as a percentage. B(y) =

You invest B, dollars in an account that draws interest at a monthly rate of r as a decimal, compounded monthly. After t months, the balance in dollars is given by the following. B- B,(1 + r)t (a) Let a denote the APR as a decimal. Then the monthly rate as a decimal is equal to a divided by 12. Express the balance in terms of the initial investment, the number of months, and the APR as a decimal. B(t) - (b) Let a denote the APR as a decimal, and let A denote the APR as a percentage. Then a is equal to A divided by 100. Express the balance in terms of the initial investment, the number of months, and the APR as a percentage. B(t) - (c) Note that y years is equivalent to 12y months. Express the balance in terms of the initial investment, the number y of years, and the APR as a percentage. B(y) =

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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The effective rate of interest compounded quarterly is given by i(m)/m. What is m? Write your answer as an integer.
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Suppose you deposit D dollars at the beginning of each month into an account that pays a monthly rate of r as a decimal. Then, the balance B of the account after t months is given by B = D(1 + r) (1 + r)t − 1 r dollars. Suppose you deposit $160 at the beginning of each month into an account that pays a monthly rate of r = 0.005, which corresponds to an APR of 6%. How long does it take for the account balance to build to $2600? Report your answer to the nearest whole month. months
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The value of a bank account collecting interest which is continuously compounded is modeled by the equation: A = Pet where: A is the value of the account at time t P, or the principal, is the value of the initial investment t is time (measured in years) r is the interest rate (written as a decimal) 1. Suppose that $5000 is put into an account with an interest rate of 8% compounded continuously. a) How much will the account be worth after 3 years (exact value) ? b) How much will the account be worth after 3 years (rounded to the nearest cent) ? c) How many years will it take for the value of the account to double? In an exponential model for population growth, the size of a population at time t is rt described by the equation: N(t) = Net where: N is the initial population or the population at t=0 r is the percentage growth rate t = time and can be measured in different units depending on the problem. Note: You don't have to use e and r. It is often possible to find an equivalent form…
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Suppose you invest $1,500 in an account paying 6% interest per year. How much of this balance corresponds to interest on interest earned in the last (7th) period? (Dollar figures should be approximated to the nearest cent of a dollar, while rates should be expressed in percentage terms without using the "%" symbol and approximated to the nearest second decimal place.)

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