(4 marks, difficulty level: Easy) Suppose that you invest $28,000 in an account paying 8% interest. You plan to withdraw $2300 at the end of each year for 20 years. How much money will be left in the account after 20 years?

Question

(4 marks, difficulty level: Easy) Suppose that you invest $28,000 in an account paying 8% interest. You plan to withdraw $2300 at the end of each year for 20 years. How much money will be left in the account after 20 years?

BlackTom AI · Accepted Answer

Question restatement: An initial deposit of $28,000 earns 8% interest per year, and you withdraw $2,300 at the end of each year for 20 years. After 20 years, how much remains in the account?

Option-by-option analysis:
- Option A: $22,361
  This value is substantially lower than the expected remaining balance. If you apply the standard future value-with-withdrawals formula, you would expect the balance to stay above the initial amount after many years because the interest (8%) compounds on the existing balance, and withdrawals are fixed. A balance this low suggests either a much larger withdrawal or a much smaller interest effect, neither of which matches the given data.
- Option B: $25,254
  This aligns closely with the correct calculation. Using the closed-form expression for the balance after n years with a starting principal P0, interest rate i, and annual withdrawal W is B_n = P0*(1+i)^n − W * [((1+i)^n − 1)/i]. Substituting P0 = 28,000, i = 0.08, W = 2,300, n = 20 gives B_20 ≈ 28,000*(1.08)^20 − 2,300 * [((1.08)^20 − 1)/0.08], which evaluates to about $25,254. The calculation uses (1.08)^20 ≈ 4.663, leading to the approximate result B_20 ≈ 130,564 − 105,310 ≈ 25,254.
- Option C: $26,371
  This is somewhat higher than the correct value. It would occur if either the future value factor (1.08)^20 were underestimated or the accumulated value of withdrawals were underestimated. Since the standard formula yields around 25,254, this option overstates the remaining balance by a modest amount, indicating a miscalculation in the substitution or rounding.
- Option D: $11,424
  This is far too small relative to the starting amount and the interest earned. Maintaining even modest compounding at 8% for 20 years without withdrawals would already exceed 11,424 by a large margin, and with withdrawals of 2,300 per year, the balance would not drop to such a low figure in this scenario.

Summary: The problem uses the standard balance-after-n-years with annual withdrawals model: B_n = P0*(1+i)^n − W * [((1+i)^n − 1)/i]. Plugging in P0 = 28,000, i = 0.08, W = 2,300, n = 20 yields approximately 25,254, which matches Option B. The other options either underestimate, overestimate, or are far from the computed value due to incorrect application or rounding of the formula.

FINE 2000 A, B & C Midterm Quiz-All Sections - F2025- Requires Respondus LockDown Browser

(4 marks, difficulty level: Easy) Suppose that you invest $28,000 in an account paying 8% interest. You plan to withdraw $2300 at the end of each year for 20 years. How much money will be left in the account after 20 years?

View Explanation

Log in for full answers

Similar Questions

Which type of annuity has payments that occur at the beginning of the period?

Which of the following best describes the difference between an annuity due and an ordinary annuity?

Which of the following statements is correct?

An annuity investment is formed when $500,000 is invested at a rate of interest of 3.1% per annum, compounded monthly.An additional payment of $1500 is made into the account each month. The value of the annuity after 5 years is closest to:

An ordinary annuity is best defined as:

An ordinary annuity is best defined as:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler