When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 7 years when $3000 is deposited in a savings account drawing 52% annual interest compounded continuously. (Round your answer to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years (c) Use a calculator to compare the amount obtained in part (a) with the amount S = - 3000(1+1 (0.0575))"(*) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) S=$

When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 7 years when $3000 is deposited in a savings account drawing 52% annual interest compounded continuously. (Round your answer to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years (c) Use a calculator to compare the amount obtained in part (a) with the amount S = - 3000(1+1 (0.0575))"(*) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) S=$

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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When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 3 years when $6000 is deposited in a savings account drawing 5 3 4 % annual interest compounded continuously. (Round your answer to the nearest cent.) b) in how many years will the initial sum deposited have doubled?(round to the nearest year) c) use a calculator to compare the amount obtained in part (a) with the amount s=(1 + 1/4(0.0575))^3(4) that is accrued when interest is compounded quarterly. (round your answer to the nearest cent.)
1.) What is the rate annually that will produce the same amount of interest per year is called? 2.) Its the total amount to be paid or received after a given period of time? 3.) What do you call the number of conversion that take place in a year 4.) What do you call the time interval between succeeding interest calculations?
The Future value of a Present amount of money (compounded annually) after 1 year can be determined by: multiplying the Present amount by (1+interest rate) dividing the Present amount by (1+interest rate) adding the interest rate to the Present amount subtracting the interest rate from the Present amount
A certain some of money P draws interest compounded continuously. If a certain time there are Po dollars in the account, determine the time when the financial attains the value of 2Po dollars if the annual interest rate at 2%
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. (/= interest rate, and n= number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1. PV of $1. FVA of $1. PVA of $1. EVAD of $1 and PVAD of $1) 1. $ 2 3 4. 15 Present Value Answer is complete but not entirely correct. Annuity Amount 2.200 145,000 190,000 72.523 45,787 8,784 558,865 480,945 520,000 240,000 8% 1.0% 9% 2.5% 10% n= 5 4 30 8 4
1. Suppose a deposit of R dollars is made at the end of each year, and assume an APR of r% compounding continuously. (a) If we invest like this for 3 years, what is the value of the account after the third year? (b) If we are making these payments for 3 years, how much money must we invest today to cover the payments? (c) If we make these payments in perpetuity, find a formula which describes the amount of principal we must invest today to cover all future payments. (d) If we invest like this for three years, but instead use an account with an APR s% compounded weekly, determine s so that this second account has the same value as your answer in part (a) after three years.
For each of the following situations involving single amounts, solve for the unknown (?). Assume that interest is compounded annually. (i = interest rate, and n = number of years) Present Value Future Value i n1. ? $ 40,000 10% 52. $ 36,289 65,000 ? 103. 15,884 40,000 8 ?4. 46,651 100,000 ? 85. 15,376 ? 7 20
For each of the following situations involving annulties, solve for the unknown. Assume that interest is compounded annually and that all annulty amounts are received at the end of each period. (/= Interest rate, and n = number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) 1. 2. 3. 4. 5. Present Value 248, 196 442,750 650,000 175,000 Annuity Amount $ 5,000 80,000 60,000 155,040 8% 11% 10% n = 5 4 10 4
For the following exercise, use the compound interest formula, A(t) = P 1 + r n nt , where money is measured in dollars.After a certain number of years, the value of an investment account is represented by the expression 10,950 1 + 0.03 2 24 . How many years had the account been accumulating interest? yr
1. (See image), which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r), expressed as a decimal for the time (t), in years is given by the function. Thus if you invested $100 now at the annual rate of 5 1/2% for 6 years and 3 months you would get back (at the end of the time), F = $100e^(0.055)^(6.25) = $100e^(0.3438) = $100(1.4102) = $141.02. Suppose you put $2000 in a savings account when your son was born for 18 years and 6 months to help pay for his college education. If you can earn 3% annually on it, what should you have in his education savings account in 18 years and 6 months?
(a) Find the present and future value of an income stream of $6000 per year for a period of 10 years if the interest rate, compounded continuously, is 2%. Round your answers to two decimal places. Present value = $ Future value $ (b) How much of the future value is from the income stream? How much is from interest? Round your answers to two decimal places. The amount from the income stream is $ The amount from the interest is $
hello for this question may someone let me know how to correctly plug in the formula to get a final answer of (11.90) as stated in the picture? (11.90) 1. question states: The doubling function D(r)=ln2ln(1+r) gives the number of years required to double your money when it is invested at interest rate r (expressed as a decimal), compounded annually. How long does it take to double your money at each of the following rates?

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