Finance. A person wishes to have $ 22,100 cash for a new car 4 years from now. How much should be placed in an account​ now, if the account pays 4.1 % annual interest​ rate, compounded​ weekly?
Use the compound interest formula and double check all calculations. Be sure that the order of operations was followed.





To find how much should be placed in an account now (the present value, $ P $) to reach a future value of $ 22,100 $ after 4 years, given an annual interest rate of $ 4.1\% $ compounded weekly, we use the compound interest formula:

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

Where:
- $ A $ is the future value (which is $22,100),
- $ P $ is the present value (what we're solving for),
- $ r $ is the annual interest rate (4.1% or 0.041),
- $ n $ is the number of times the interest is compounded per year (weekly compounding means $ n = 52 $),
- $ t $ is the time in years (4 years).

Rearranging the formula to solve for $ P $:

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

Now let's plug in the values and calculate $ P $.

\[
P = \frac{22100}{\left( 1 + \frac{0.041}{52} \right)^{52 \times 4}}
\]

I will compute this step-by-step.The amount that should be placed in the account now is approximately **$18,758.41** in order to reach $22,100 after 4 years with a 4.1% annual interest rate compounded weekly.

Would you like more details or have any other questions?

Here are 5 related questions to consider:
1. What would the present value be if the interest were compounded monthly instead of weekly?
2. How much interest will the account earn over the 4 years?
3. What if the interest rate were 5% instead of 4.1%—how would that affect the present value?
4. How would the calculation change if the interest were compounded continuously?
5. What is the difference in the final amount if you compounded interest annually instead of weekly?

**Tip:** Always ensure you check the compounding frequency when planning investments, as more frequent compounding can significantly increase the future value!

Finance. A person wishes to have $22,100 cash for a new car 4 years from now. How much should be placed in an account​ now, if the account pays 4.1% annual interest​ rate, compounded​ weekly?

Learn how to calculate how much money should be placed in an account today to reach $22,100 in 4 years, with a 4.1% interest rate compounded weekly. This finance-related problem uses the compound interest formula, making it ideal for students in Grades 11-12.

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