A person wishes to have

$ 15 comma 700$15,700

cash for a new car

44

years from now. How much should be placed in an account​ now, if the account pays

5.9 %5.9%

annual interest​ rate, compounded​ weekly?

To determine how much should be placed in an account now to have $15,700 in 44 years, given a 5.9% annual interest rate compounded weekly, we can use the **compound interest formula**:

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

Where:
- $A$ = future value ($15,700),
- $P$ = present value (the amount we need to find),
- $r$ = annual interest rate (5.9% or 0.059),
- $n$ = number of times the interest is compounded per year (weekly, so $n = 52$),
- $t$ = time in years (44 years).

Rearranging the formula to solve for $P$:

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

Now, we can plug in the values:

\[
P = \frac{15,700}{\left(1 + \frac{0.059}{52}\right)^{52 \times 44}}
\]

Let me calculate that for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to walk you through the manual calculations or explain the concept further?

Here are 5 questions that expand on this concept:

1. How does weekly compounding differ from monthly compounding in interest calculations?
2. What would the result be if the interest was compounded yearly instead of weekly?
3. How would the initial deposit change if the interest rate were lower, say 4%?
4. Can you apply the same formula for different types of accounts, like savings or retirement?
5. What happens to the amount required if the investment period is shorter, say 20 years instead of 44?

**Tip:** Always double-check your interest rate's compounding frequency, as different rates can lead to significantly different results.

A person wishes to have $15,700 cash for a new car 44 years from now. How much should be placed in an account now, if the account pays 5.9% annual interest rate, compounded weekly?

Discover how much needs to be invested today to have $15,700 in 44 years using a 5.9% annual interest rate compounded weekly. This problem uses the compound interest formula and is suitable for students in Grades 10-12 learning about exponential growth and financial mathematics.

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