Question
upstudy study bank question image url

At the age of 27 , to save for retirement, you decide to deposit \( \$ 70 \) at the end of each month in an IRA that pays \( 4 \% \) compounded monthly. a. Use the following formula to determine how much you will have in the IRA when you retire at age 65 . \[ A=\frac{P\left[(1+r)^{t}-1\right]}{r} \text { or } \] \[ A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} \] b. Find the interest.

Ask by Davey Patel. in the United States
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

After 38 years, the IRA will have approximately \$74,760. The interest earned is approximately \$42,840.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

To determine how much you'll have in the IRA when you retire at age 65 using the given formula, let's plug in the numbers: 1. **Monthly Deposit (P):** $70 2. **Annual Interest Rate (r):** 4% or 0.04 3. **Months in a Year (n):** 12 4. **Total Investment Duration (t):** 65 - 27 = 38 years Now we can calculate \( A \): \[ A = \frac{70\left[\left(1+\frac{0.04}{12}\right)^{12 \times 38}-1\right]}{\left(\frac{0.04}{12}\right)} \] Calculating the components: - \( \frac{0.04}{12} = 0.003333 \) - \( 12 \times 38 = 456 \) - \( 1 + 0.003333 = 1.003333 \) - \( \left(1.003333\right)^{456} \approx 4.0688 \) Putting this all together: \[ A \approx \frac{70\left[4.0688-1\right]}{0.003333} \approx \frac{70 \times 3.0688}{0.003333} \approx \frac{214.816}{0.003333} \approx 64,445.15 \] So, you'll have about **$64,445.15** in the IRA when you retire at age 65. To find the interest earned, subtract the total contributions from the total amount in the IRA: - **Total Contributions:** \( 70 \times 12 \times 38 = 70 \times 456 = 31,920 \) - **Interest Earned:** \( 64,445.15 - 31,920 = 32,525.15 \) Therefore, the interest earned will be approximately **$32,525.15**.

Related Questions

2 QUESTION 1 : CONCEPTS,JOURNALS AND POSTING (78 marks; 70 Minutos) 1.1. CONCEPTS REQUIRED: Indicate whether the following statements are TRUE or FALSE. Write only 'true' or 'false' next to the question number (1.1.1-1.1.5). 1.1.1 Trading stock, bank and debtors are examples of non-current assets. (1) 1.1.2 A bank overdraft is a facility that allows the business to use more money than they have in their current banking account. (1) 1.1.3 Non-current liabilities are payable within a period of one year. 1.1.4 A creditor is a person or business that is owed money for goods or services they supplied on credit. 1.1.5 Equipment such as a cash register and printers are used to generate income for the business. 1.2 CASH JOURNALS JADE CREATIONS The following information was taken from the books of Jade Creations for March 2021. Jade Creations uses a mark-up of \( 60 \% \) for all merchandise sold. REQUIRED: 1.2.1 Complete the following Journals in the financial records of Jade Creations for March 2021: - Cash Receipts Journal - Cash Payments Journal 1.2.2 Post to the Bank Account in the General Ledger. Balance the account at the end of March 2021. Note: The opening balance is recorded in the answer book. RANSACTIONS FOR MARCH 2021 Paid Thato Suppliers for trading stock, R12 800 and stationery, R350 (EFT 190). Cash sales for the week amounted to R6 520 (CRR 01). Received an EFT 05 from R Rose for the rent for March 2021, R5 300. Invested R20 000 in a fixed deposit at UK Bank at an interest of \( 9 \% \) per annum, (EFT 191). Transferred weekly wages to the account of Sheila, R2 500, and EFT 192. Grade 10 Controlled test-Question paper 07 April 2021

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