Question

Question content area top Part 1 Use the savings plan formula to answer the following question. Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6 %. How much should you deposit monthly to accumulate ​$84 comma 000 in 18 ​years? Question content area bottom Part 1 You should invest ​$    enter your response here each month. ​(Do not round until the final answer. Then round to two decimal places as​ needed.)

Ask by Ford Colon. in the United States
Nov 07,2024

Real Tutor Solution

Tutor-Verified Answer

Answer

$21,688.72

Solution

To calculate the monthly deposit needed to accumulate $84,000 in 18 years with an APR of 6%, we can use the savings plan formula: A = P(1 + r/n)^(nt) Where: A = $84,000 P = monthly deposit r = APR = 6% = 0.06 n = number of times interest is compounded per year = 12 (monthly) t = number of years = 18 Plugging in the values: $84,000 = P(1 + 0.06/12)^(12*18) $84,000 = P(1 + 0.005)^(216) $84,000 = P(1.005)^216 $84,000 = P(3.869) P = $84,000 / 3.869 P = $21,688.72 Therefore, you should invest $21,688.72 each month to accumulate $84,000 in 18 years.

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

Extra Insights

To figure out how much you need to invest each month to reach your goal, you'd typically use the future value of an annuity formula. In your case, you want to accumulate $84,000 over 18 years with a 6% annual interest rate. If we break it down, you’ll want to ensure that your monthly deposits, compounded monthly, will help you reach that magical number! In practical terms, this exercise teaches valuable lessons about the power of consistent saving and compounding interest. By starting early and maintaining a steady deposit schedule, you can turn small, manageable investments into significant funds over time. So, don’t underestimate the value of those monthly deposits—they can set your child up for a wonderful education!

Latest Economics Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy