How much must be deposited today into the following account in order to have

$ 55 comma 000$55,000

in

55

years for a down payment on a​ house? Assume no additional deposits are made.

An account with monthly compounding and an APR of

88​%

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Part 1

​$enter your response here

should be deposited today.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To solve this problem, we need to determine the present value $ P $ that must be deposited today to grow to $55,000 in 55 years with monthly compounding and an APR of 8%. We use the following present value formula for compound interest:

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

Where:
- $ A = 55,000 $ is the amount we want in the future (the future value).
- $ r = 0.08 $ is the annual interest rate (APR = 8%).
- $ n = 12 $ is the number of times the interest is compounded per year (monthly compounding).
- $ t = 55 $ years is the time period.

Let's plug the values into the formula and calculate.

\[
P = \frac{55,000}{(1 + \frac{0.08}{12})^{12 \times 55}}
\]

I'll compute this now.The amount that must be deposited today is approximately **$685.19**.

Would you like more details, or do you have any other questions?

Here are 5 related questions:
1. How would the result change if the APR were 6% instead of 8%?
2. What is the effect of quarterly compounding rather than monthly compounding?
3. How much interest would be earned over the 55 years in this scenario?
4. What would be the future value if $685.19 were deposited today at 8% for only 30 years?
5. How does simple interest compare to compound interest in long-term investments?

**Tip:** Compound interest grows faster than simple interest because interest is calculated on both the initial principal and the accumulated interest.

How much must be deposited today into the following account in order to have $55,000 in 55 years for a down payment on a house? Assume no additional deposits are made. An account with monthly compounding and an APR of 8%.

Learn how to calculate the present value needed to accumulate $55,000 in 55 years with monthly compounding and an APR of 8%. This detailed solution covers key concepts in compound interest and present value calculations, suitable for high school students in Grades 10-12.

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