**Interest Compounding Comparison Exercise****Introduction:**This exercise evaluates the future value of investments with two banks offering different interest rates and compounding frequencies. Understanding which option yields a higher return can guide financial decision-making.**Scenario:**- **First National Bank** offers 5.3% interest compounded semiannually.- **Second National Bank** offers 6% interest compounded monthly.**Instructions:**a. **Calculate the Future Value with First National Bank** - Assume an investment of $1. - Perform calculations without rounding intermediate results. - Provide the final answer rounded to five decimal places. - **Future value for First National Bank:** - Input your result here: $ _______b. **Calculate the Future Value with Second National Bank** - Assume an investment of $1. - Perform calculations without rounding intermediate results. - Provide the final answer rounded to five decimal places. - **Future value for Second National Bank:** - Input your result here: $ _______c. **Determine the Better Investment** - Identify which bank offers the higher effective annual rate. - Choose one of the following options: - ⭕ First National Bank - ⭕ Second National Bank**Objective:**This exercise helps in analyzing the impact of different compounding methods on investment returns, highlighting the importance of understanding effective interest rates in financial planning.

FV =PV(1+rm)nm n = no of years m = no of compounding in year

First National Bank pays 5.3% interest compounded semiannually. Second National Bank pays 6% interest, compounded monthly. a. Calculate the future value for each dollar invested in First National (Assume you invest $1). (Do not round intermediate calculations. Round your answer to 5 decimal places.) Future value b. Calculate the future value for each dollar invested in Second National (Assume you invest $1). (Do not round intermediate calculations. Round your answer to 5 decimal places.) Future value c. Which bank offers the higher effective annual rate? O First National Bank O Second National Bank

First National Bank pays 5.3% interest compounded semiannually. Second National Bank pays 6% interest, compounded monthly. a. Calculate the future value for each dollar invested in First National (Assume you invest $1). (Do not round intermediate calculations. Round your answer to 5 decimal places.) Future value b. Calculate the future value for each dollar invested in Second National (Assume you invest $1). (Do not round intermediate calculations. Round your answer to 5 decimal places.) Future value c. Which bank offers the higher effective annual rate? O First National Bank O Second National Bank

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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Bank 1 is offering interest rate of 8.4% (compounds semiannually) on fixed deposits. Beck 2 is offering interest rate of 8.3% (compounds monthly) on fixed deposits. An investor invested amount of $15,000 for five years in the bank that is offering highest effective annual rate. What is the accumulated amount at the end of five years? a $22,683 b. $22.634 c. $22.451 d $22.982
a) A bank made a 4-year 12% amortizing $2,500,000 loan with equal payments. What is the amount of interest and principal paid at the end of the 3rd year? What is the balance on the loan at the end of the 3rd year? b) Assume instead the bank demands that the borrower pay interest only for the first two years and then principal payments of $1,250,000 in years 3 and 4. What is the amount of interest and principal paid at the end of the 3rd year? What is the balance on the loan at the end of the 3rd year? Assume the same 12% rate of interest. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
First City Bank pays 5 percent simple interest on its savings account balances, Second City Bank pays 5 percent interest compounded annually. If you made a deposit of $13,500 in each bank, how much more money would y from your Second City Bank account at the end of 11 years? (Do not round inter calculations and round your answer to 2 decimal places, e.g., 32.16.) Difference
Compute the present value of a $2,000 deposit in year 1, and another $2,500 deposit at the end of year 4 using an 8 percent interest rate. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
Suppose you deposit $1,751.00 into an account today that earns 5.00%. It will take ___ years for the account to be worth $2,806.00. Answer format: Number: Round to: 2 decimal places.
= A bank features a savings account that has an annual percentage rate of r interest compounded quarterly. Tatiana deposits $9,000 into the account. The account balance can be modeled by the exponential formula A(t) = a (1 + 7-)kt, where A is account value after t years, a is the principal (starting amount), r is the annual percentage rate, k is the number of times each year that the interest is compounded. (A) What values should be used for a, r, and k? a = r = 5.6% with k = (B) How much money will Tatiana have in the account in 7 years? Answer = $ 7. Round answer to the nearest penny. APY = = %. Round answer to 3 decimal places. (C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year).
1) Let y be the balance in an account if you deposit $5000 for x years at 4% APR compounded monthly. USE ALL DECIMALS except in e and fand h! a) Write the formula for y = f(x) b) Then rewrite the formula as an annual compounding (APY) formula as shown in the Lecture 16 notes. y = (rewritten). c) The APY (clear from part b) is: d) Then use the 2âd version of y to write y ' - e) How much is the investment worth after 7 years? f) How fast is the investment growing after 7 years? g) What is the percentage rate of growth (PROC) after 7 years as a percent? USE ALL DECIMALS! h) Write a sentence translating into English your answer for f' (7) : i) Show the second way to find the derivative of your formula in a) using the chain rule (as found in the chain rule lecture): j) Find y'(7) from your answer in j and confirm it is the same (at least to 7 decimals) as using the formula in d.
Assume Sheffield Corp. deposits $81000 with First National Bank in an account earning interest at 4% per annum, compounded semi-annually. How much will Sheffield have in the account after 4 years if interest is reinvested? O $94904. O $81000. O $93960. O $94760.
Answers seen in the blanks right now are not correct.
None
Compute the future value in year 7 of a $2,200 deposit in year 1, and another $1,700 deposit at the end of year 4 using a 8 percent interest rate. Note: Do not round intermediate calculations and round your final answer to 2 decimal places. Future value $ 3,770.41
S You deposit $1,200 in your bank account. a. If the bank pays 5% simple interest, how much will you accumulate in your account after 8 years? Future value Saved b. How much will you accumulate if the bank pays compound interest? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Future value M Question 7

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