The force of interest, ε(t), is a function of time and at any time t (measured in years) is given by8(t)(0.1-0.006tfor t≤8=0.052for t> 8Calculate the accumulation at time t = 16 of £500 invested at time t = 0.£ 数字Enter a value correct to 2 decimal places.

Step 1: The initial expression is a sum of two terms: (Pe^{\int_{5}^{t} (0.06 - 0.001t) dt}) and…

Answered: The force of interest, ε(t), is a…

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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Jus part I) and Ii)
3. * The force of interest (t) at time t (measured in years) is a + bt² where a and b are constants. An amount of £200 at time t = 0 accumulates to £210 at t = 5 and £230 at t = 10. 1 (a) Show that a = log (1.05) - 30 log(1.15) = 0.008352, and b = 250 log(1.15) - 125 log(1.05) = 0.0001687. (b) Compute A(0, 7) and hence compute the discounted value at t = 0 of a payment of £750 due at t = 7. (c) Compute A(6, 7). What is the equivalent constant annual interest rate for the year from t = 6 to t = 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from t = 0 to t = 10.
An investment is represented by the equation A(t)=10,250(1+ 0.04/12)120 How many years has the account been accumulating interest?
Compute the number of years (t) if future value (FV) = $12,029, present value (FV) = $1,826, and interest rate (r) = 9%,. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.):
Solve for the unknown interest rate in each of the following: (Do 2 decimal places.) Present Value Years $ 310 4 430 18 19 25 39,700 38,961 Interest Rate olo oo oo Future Value 388 $ 1,430 186,082 538,618
3. * The force of interest 8(t) at time t (measured in years) is a+bt² where a and b are constants. An amount of £200 at time t and £230 at t = 10. = 0 accumulates to £210 at t = 5 (a) Show that 1 4 a = 15 1 b = 250 log (1.05) log (1.15) - 3 log(1.15) 0.008352, 1 125 = log (1.05) = 0.0001687. and (b) Compute A(0, 7) and hence compute the discounted value at t = 0 of a payment of £750 due at t = 7. (c) Compute A(6, 7). What is the equivalent constant annual interest rate for the year from t = 6 to t = 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from t = 0 to t = 10.
The total amount of money in an account with P dollars invested in it is given by the formula A=P+PrtA=P+Prt, where r is the rate expressed as a decimal and t is time (in years).If $525$⁢525 is invested at 14%14%, how much money will be in the account after 3030 months? Round your answer to two decimal places if necessary.
For each of the following compute the present value.
For each of the following, compute the present value: (Do not round inte calculations and round your answers to 2 decimal places, e.g., 32.16.) Present Value Years 12 4 16 21 Interest Rate 4 % 9 12 11 Future Value $ 18,528 42,717 802,382 659,816
Complete the following table. Use Exhibit 1-B. (Round time value factors to 3 decimal places and final answers to the nearest whole number.) Annual Deposit Rate of Return Number of Years Investment Value at the End of Time Period Total Amount of Investment Total Amount of Interest or Earnings $1,800 8 % 9 $22,478 $1,800 12 % 9 $1,800 8 % 18 $1,800 12 % 18
For each of the following, compute the future value: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present Value $ 1,900 8,052 69.355 176.796 Years 6 7 Interest Rate 12 % 10 % 11 % Future Value
For each of the following, compute the present value (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future Value 12 6 % $ 15,951 3 12 56,557 28 13 891,073 30 10 555,164

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The force of interest, ε(t), is a function of time and at any time t (measured in years) is given by 8(t) (0.1-0.006t for t≤8 = 0.052 for t> 8 Calculate the accumulation at time t = 16 of £500 invested at time t = 0. £ 数字 Enter a value correct to 2 decimal places.