### Investment Problem **Question:** Sally Ross has $19,000 to invest today at 9% to pay a debt of $37,859. How many years will it take her to accumulate enough to liquidate the debt? *(Round answer to 0 decimal places, e.g., 45.)* **Input Box:** - [___________] years #### Explanation: This problem involves calculating the time required for an investment to grow to a certain amount using a specified interest rate. Sally aims to accumulate sufficient funds with an initial investment of $19,000 at an annual interest rate of 9% to pay off a debt of $37,859. The solution requires using the formula for compound interest: \[ A = P(1 + r)^t \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount ($19,000 in this case). - \( r \) is the annual interest rate (0.09 here). - \( t \) is the time the money is invested for in years. The task is to find \( t \) when \( A = 37,859 \).

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
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### Investment Problem

**Question:**

Sally Ross has $19,000 to invest today at 9% to pay a debt of $37,859. How many years will it take her to accumulate enough to liquidate the debt? *(Round answer to 0 decimal places, e.g., 45.)*

**Input Box:**

- [___________] years

#### Explanation:

This problem involves calculating the time required for an investment to grow to a certain amount using a specified interest rate. Sally aims to accumulate sufficient funds with an initial investment of $19,000 at an annual interest rate of 9% to pay off a debt of $37,859.

The solution requires using the formula for compound interest:

\[ A = P(1 + r)^t \]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($19,000 in this case).
- \( r \) is the annual interest rate (0.09 here).
- \( t \) is the time the money is invested for in years.

The task is to find \( t \) when \( A = 37,859 \).
Transcribed Image Text:### Investment Problem **Question:** Sally Ross has $19,000 to invest today at 9% to pay a debt of $37,859. How many years will it take her to accumulate enough to liquidate the debt? *(Round answer to 0 decimal places, e.g., 45.)* **Input Box:** - [___________] years #### Explanation: This problem involves calculating the time required for an investment to grow to a certain amount using a specified interest rate. Sally aims to accumulate sufficient funds with an initial investment of $19,000 at an annual interest rate of 9% to pay off a debt of $37,859. The solution requires using the formula for compound interest: \[ A = P(1 + r)^t \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount ($19,000 in this case). - \( r \) is the annual interest rate (0.09 here). - \( t \) is the time the money is invested for in years. The task is to find \( t \) when \( A = 37,859 \).
Expert Solution
Step 1

It can be calculated using Nper function in excel

=NPER(rate,pmt,pv,[fv],[type])

  • Rate The interest rate for the loan.
  • Nper  The total number of payments for the loan.
  • Pmt payment per period
  • Pv    The present value
  • Fv  The future value
  • Type The number 0 (zero) or 1 and indicates when payments are due.
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