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 for simple interest, we use the formula:
Where:
- is the future value (the amount you want to have),
- is the present value (the amount to be invested),
- is the annual interest rate (in decimal form),
- is the time in years.
Step 1: Convert the given information
- (as a decimal)
- months = years (since there are 12 months in a year)
Step 2: Rearrange the formula to solve for :
Step 3: Plug in the known values:
Final Answer:
The present value that must be invested is $8610.24.
Would you like further clarification on any of the steps, or have other questions?
Related Questions:
- How does the interest rate impact the amount that must be invested to reach a certain future value?
- What would happen to the present value if the time period increased to 5 years?
- How can you calculate the future value for different interest rates and time periods?
- What is the formula for calculating interest using compound interest instead of simple interest?
- 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
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