Math Problem Statement

Determine the present value P that must be invested to have the future value A at simple interest rate r after time t.

A​ =

​$90009000​,

r​ =

1.651.65​%,

t​ =

33

months

Question content area bottom

Part 1

The present value P that must be invested is

​$enter your response here.

​(Round up to the nearest​ cent.)

Solution

To determine the present value PP for simple interest, we use the formula:

A=P(1+rt)A = P \left(1 + r t \right)

Where:

  • AA is the future value (the amount you want to have),
  • PP is the present value (the amount to be invested),
  • rr is the annual interest rate (in decimal form),
  • tt is the time in years.

Step 1: Convert the given information

  • A=9000A = 9000
  • r=1.65%=0.0165r = 1.65\% = 0.0165 (as a decimal)
  • t=33t = 33 months = 3312=2.75\frac{33}{12} = 2.75 years (since there are 12 months in a year)

Step 2: Rearrange the formula to solve for PP:

P=A1+rtP = \frac{A}{1 + r t}

Step 3: Plug in the known values:

P=90001+0.0165×2.75P = \frac{9000}{1 + 0.0165 \times 2.75}

P=90001+0.045375P = \frac{9000}{1 + 0.045375}

P=90001.045375P = \frac{9000}{1.045375}

P8610.24P \approx 8610.24

Final Answer:

The present value PP that must be invested is $8610.24.

Would you like further clarification on any of the steps, or have other questions?

Related Questions:

  1. How does the interest rate impact the amount that must be invested to reach a certain future value?
  2. What would happen to the present value if the time period increased to 5 years?
  3. How can you calculate the future value for different interest rates and time periods?
  4. What is the formula for calculating interest using compound interest instead of simple interest?
  5. How can you apply the same formula to calculate the present value of an investment with monthly interest?

Tip:

When working with simple interest, remember that the interest is calculated on the initial principal amount only and does not compound. This makes it simpler to calculate compared to compound interest.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Algebra

Formulas

A = P(1 + rt)
P = A / (1 + rt)

Theorems

Simple Interest Theorem

Suitable Grade Level

Grades 9-12