You deposit $2000 in an account that pays 7% interest compounded semiannually. After 2 years, the interest rate is increased to 7.52% compounded quarterly. What will be the value of the account after a total of 4 years? Click the icon to view some finance formulas. The value of the account will be $ (Round to the nearest dollar as needed.)
You deposit $2000 in an account that pays 7% interest compounded semiannually. After 2 years, the interest rate is increased to 7.52% compounded quarterly. What will be the value of the account after a total of 4 years? Click the icon to view some finance formulas. The value of the account will be $ (Round to the nearest dollar as needed.)
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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![In the provided formulas, A is the balance in the account after t years, P is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and Y is the investment's effective annual yield in decimal form.
- Formula for balance after t years:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
- Formula for principal investment:
\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]
- Continuous compounding formula for balance:
\[
A = Pe^{rt}
\]
- Formula for effective annual yield:
\[
Y = \left(1 + \frac{r}{n}\right)^n - 1
\]
These formulas illustrate the calculations for compound interest where the principal amount is invested to accrue interest over time, with varying compounding periods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7e7854b-0be5-41c7-9658-968f15b06285%2Fac6c18c7-a1d7-4bbb-9fd7-b75b3c9e7570%2F7j7pl2e_processed.png&w=3840&q=75)
Transcribed Image Text:In the provided formulas, A is the balance in the account after t years, P is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and Y is the investment's effective annual yield in decimal form.
- Formula for balance after t years:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
- Formula for principal investment:
\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]
- Continuous compounding formula for balance:
\[
A = Pe^{rt}
\]
- Formula for effective annual yield:
\[
Y = \left(1 + \frac{r}{n}\right)^n - 1
\]
These formulas illustrate the calculations for compound interest where the principal amount is invested to accrue interest over time, with varying compounding periods.
Transcribed Image Text:**Investment Scenario:**
You deposit $2000 in an account that pays 7% interest compounded semiannually. After 2 years, the interest rate is increased to 7.52% compounded quarterly. What will be the value of the account after a total of 4 years?
**Finance Calculations:**
- Click the icon to view some finance formulas.
**Final Calculation:**
The value of the account will be $ ____.
*(Round to the nearest dollar as needed.)*
---
In this exercise, you’ll calculate the future value of an investment with changing interest rates and compounding frequencies. You initially invest $2000 with different conditions over 4 years. Use financial formulas to determine the final account value after accounting for interest rate adjustments and compounding differences.
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