Math Problem Statement

What amount of money was borrowed on July 17, 2010, if the final amount is $6,370.72 paid off on November 25, 2018, with a 2.9% interest rate compounded monthly?

Solution

The problem presented in the image asks for the amount of money borrowed on July 17, 2010, based on a final loan amount of $6,370.72 paid off on November 25, 2018, with a 2.9% interest rate compounded monthly.

Step-by-step solution:

  1. Formula: The formula for compound interest is:

    A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}

    Where:

    • AA is the final amount ($6,370.72).
    • PP is the principal amount (what we need to find).
    • rr is the annual interest rate (2.9% or 0.029).
    • nn is the number of times the interest is compounded per year (monthly, so n=12n = 12).
    • tt is the time in years (from July 17, 2010, to November 25

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Functions
Algebra

Formulas

A = P (1 + r/n)^(nt)

Theorems

Compound Interest Formula

Suitable Grade Level

Grades 10-12