Math Problem Statement
An initial investment of
$
1
,
000
at
12
%
interest is compounded weekly (use
52
weeks in a year). What will the investment be worth in
30
years? Round your answer to the nearest cent.
Solution
To solve this problem, we'll use the formula for compound interest:
where:
- is the amount of money accumulated after years, including interest.
- is the principal amount (the initial investment).
- is the annual interest rate (in decimal form).
- is the number of times that interest is compounded per year.
- is the number of years the money is invested for.
Given:
- dollars
- (since the interest is compounded weekly)
- years
Let's calculate :
Now, we'll calculate the value.
The investment will be worth $36,446.76 after 30 years, when compounded weekly at a 12% annual interest rate.
Would you like further details or have any questions?
Here are some related questions you might find interesting:
- How would the final amount change if the interest were compounded daily instead of weekly?
- What would be the investment worth after 20 years instead of 30?
- How does the compound interest formula differ from simple interest?
- How would the amount change if the interest rate were 10% instead of 12%?
- How does increasing the compounding frequency affect the final investment amount?
Tip: The more frequently interest is compounded, the greater the final amount will be due to the effect of earning interest on interest more often.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Exponential Growth
Formulas
Compound Interest Formula
Theorems
-
Suitable Grade Level
High School
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