You plan to invest in securities that pay 11.2%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20? O a. 5.68 O b.4.60 c. 5.85 O d. 5.63 O e. 6.36
You plan to invest in securities that pay 11.2%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20? O a. 5.68 O b.4.60 c. 5.85 O d. 5.63 O e. 6.36
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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![**Investment Growth Calculation**
You plan to invest in securities that pay 11.2%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?
- a. 5.68
- b. 4.60
- c. 5.85
- d. 5.63
- e. 6.36
**Explanation:** To determine the number of years required for an investment to grow from its present value to a future value with compound interest, you can use the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the future value of the investment,
- \( P \) is the present value (initial investment),
- \( r \) is the annual interest rate (expressed as a decimal),
- \( n \) is the number of years.
Rearrange the formula to solve for \( n \):
\[ n = \frac{\log(A/P)}{\log(1 + r)} \]
Substitute the given values into this formula to find \( n \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ede43bb-e880-4024-8d83-4554574c0cce%2Fafde5659-c9dc-4119-9320-ca92767b3989%2F4wwcyod_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Investment Growth Calculation**
You plan to invest in securities that pay 11.2%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?
- a. 5.68
- b. 4.60
- c. 5.85
- d. 5.63
- e. 6.36
**Explanation:** To determine the number of years required for an investment to grow from its present value to a future value with compound interest, you can use the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the future value of the investment,
- \( P \) is the present value (initial investment),
- \( r \) is the annual interest rate (expressed as a decimal),
- \( n \) is the number of years.
Rearrange the formula to solve for \( n \):
\[ n = \frac{\log(A/P)}{\log(1 + r)} \]
Substitute the given values into this formula to find \( n \).
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