Andrew would like to accumulate $15,000 in his savings account at the end of 4 years. If effective annual interest rate is 11%. What would be the amount of equal deposit at the end of each year for 4 years.

Question

BlackTom AI · Accepted Answer

Future value of an ordinary annuity is used: S = R * [(1 + i)^n − 1] / i, where R is the end-of-year deposit, i = 0.11, n = 4, and S = 15,000.

1) Relevant concepts:
- Ordinary annuity (payments at the end of each period).
- Future value factor for an annuity: s_n = [(1 + i)^n − 1] / i.
- Solve for R by rearranging: R = S * i / [(1 + i)^n − 1].

2) Step-by-step reasoning and calculations:
- Compute (1 + i)^n = 1.11^4.
  1.11^2 = 1.2321
  1.11^3 = 1.2321 × 1.11 = 1.367631
  1.11^4 = 1.367631 × 1.11 = 1.51807041
- Compute (1 + i)^n − 1 = 1.51807041 − 1 = 0.51807041.
- Compute numerator S * i = 15,000 × 0.11 = 1,650.
- Solve for R: R = 1,650 / 0.51807041 ≈ 3,184.900 (rounded to cents $3,184.90).

3) Intermediate summary:
- The annuity future-value factor s_4 = 0.51807041 / 0.11 = 4.709731.
- Check: R × s_4 = 3,184.90 × 4.709731 ≈ 15,000 (confirms the calculation).

4) Why this answer is correct:
- Using the correct ordinary-annuity future-value formula with precise powers and arithmetic yields R ≈ $3,184.90, which produces the desired future value of $15,000 after 4 end-of-year deposits at 11% effective annual interest.

5) Why the other choices are incorrect:
- $4,355.76 and $4,834.90 produce future values well above $15,000 (too large payments).
- $2,869.28 produces a future value below $15,000 (too small payments).
- Only $3,184.90 yields the required $15,000 when multiplied by the annuity future-value factor 4.709731.

6) Conclusion:
The correct equal deposit at the end of each year is $3,184.90, matching the provided answer.

Andrew would like to accumulate $15,000 in his savings account at the end of 4 years. If effective annual interest rate is 11%. What would be the amount of equal deposit at the end of each year for 4 years.Single choice

Similar Questions

Study the screenshot above.Miguel invests $1500 every month for 5 years with an annual interest rate of 8.23%. What formula is needed to calculate what Miguel's investment is worth at the end of 5 years? Show as a positive number.

Question13 Suppose you receive $1,100 per year for 5 years, starting with your first payment at the end of year 1, earning a return of 6.5%. What is the FV of these cash flows approximately equal to?Select one alternative: $4,571 $10,392 $6,263 $14,441 ResetMaximum marks: 3 Flag question undefined

You plan to save for your child's education by depositing $880 at the end of each month into an account that earns an annual interest rate of 8%, compounded monthly. If you plan to invest for 12 years, calculate the value at the end of this period. Please write the answer in two decimal places.

Your goal is to accumulate $149,904 in nine years' time. What monthly deposit must you make into a savings account to reach your goal? Interest rates are 22% per annum, compounded monthly. Please write the answer in two decimal places.

You want to have $1 million to use for retirement in 35 years. If you earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month?

What will the future value be if you open the account with $1,000 today, and then make the $100 deposits at the end of each year?

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