Math Problem Statement

Fill in the missing values in the table with the given data on interest amounts, principal values, interest rates, time, and future values.

Solution

To solve this, I’ll use the formula for simple interest and compound interest based on the type of interest rate implied. Let’s walk through each row in detail.

Simple Interest Formula:

For the cases with simple interest, the formula is: A=P×(1+r×t)A = P \times (1 + r \times t) where:

  • AA = Future/Maturity Value
  • PP = Principal/Present Value
  • rr = Interest Rate per period
  • tt = Time in periods

The Interest Amount can be calculated by subtracting the principal from the maturity value: Interest Amount=AP\text{Interest Amount} = A - P

Analysis of Each Row:

Row 1:

  • Given: P=16,225.00P = 16,225.00, r=0.4%r = 0.4\% per month, t=6t = 6 months
  • Objective: Future Value (AA)

A=16,225×(1+0.004×6)=16,225×(1+0.024)=16,225×1.024=16,616.40A = 16,225 \times (1 + 0.004 \times 6) = 16,225 \times (1 + 0.024) = 16,225 \times 1.024 = 16,616.40 The Future Value should be $16,616.40.


Row 2:

  • Given: P=61,910P = 61,910, r=10%r = 10\% per year, t=4t = 4 months
  • Objective: Interest Amount

Assuming simple interest for 4 months (1/3 of a year): A=61,910×(1+0.1×412)=61,910×(1+0.0333)=61,910×1.033363,978.30A = 61,910 \times (1 + 0.1 \times \frac{4}{12}) = 61,910 \times (1 + 0.0333) = 61,910 \times 1.0333 \approx 63,978.30 The Interest Amount would be $63,978.30 - 61,910 = 2,068.30.


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Math Problem Analysis

Mathematical Concepts

Simple Interest
Compound Interest
Algebra

Formulas

Simple Interest: A = P * (1 + r * t)
Compound Interest: A = P * (1 + r)^t
Interest Amount: Interest = A - P

Theorems

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Suitable Grade Level

Grades 10-12