Question14 You feel that you will need $1.85 Million in your retirement account, and when you reach that amount, you plan to retire. You believe you can earn an APR of 9.2% compounded monthly and plan to save $420 per month until you reach your goal. How many years will it be until you reach your goal and retire? 34.18 years 38.72 years 41.56 years 45.03 years ResetMaximum marks: 2 Flag question undefined单项选择题
A
34.18 years
B
38.72 years
C
41.56 years
D
45.03 years

Question

Question14 You feel that you will need $1.85 Million in your retirement account, and when you reach that amount, you plan to retire. You believe you can earn an APR of 9.2% compounded monthly and plan to save $420 per month until you reach your goal. How many years will it be until you reach your goal and retire? 34.18 years 38.72 years 41.56 years 45.03 years ResetMaximum marks: 2 Flag question undefined单项选择题

A

34.18 years

B

38.72 years

C

41.56 years

D

45.03 years

BlackTom AI · Accepted Answer

Monthly savings accumulate according to the future value of an ordinary annuity:
FV = PMT * [ (1 + r)^n - 1 ] / r. Here PMT = $420, target FV = $1,850,000, and APR = 9.2% compounded monthly so the monthly rate r = 0.092/12.

Step-by-step solution:
1) Monthly interest rate: r = 0.092 / 12 = 0.007666666666666667.
2) Plug into the annuity formula and solve for the number of periods n:
   1,850,000 = 420 * [ (1 + r)^n - 1 ] / r
   Rearranged: (1 + r)^n = 1 + (FV * r) / PMT.
3) Compute FV * r: 1,850,000 * 0.007666666666666667 = 170,200 / 12 = 14,183.333333333334.
4) Compute (FV * r) / PMT: 14,183.333333333334 / 420 = 33.76984126984032.
   So (1 + r)^n = 1 + 33.76984126984032 = 34.76984126984032.
5) Take natural logs to solve for n:
   n = ln(34.76984126984032) / ln(1.0076666666666667).
   ln(34.76984126984032) ≈ 3.548606; ln(1.0076666666666667) ≈ 0.007637428.
   Therefore n ≈ 3.548606 / 0.007637428 ≈ 464.711 months.
6) Convert months to years: 464.711 / 12 ≈ 38.7259 years ≈ 38.72 years.

Why this is correct: the algebra and numeric evaluation directly follow the future-value formula for level end-of-period contributions with monthly compounding. The computed n gives the time required for $420 monthly deposits at 9.2% APR (monthly compounding) to accumulate to $1.85 million.

Why the other choices are incorrect: 34.18, 41.56, and 45.03 years do not satisfy the annuity equation with the given r and PMT; they are respectively too short or too long compared with the precise solution (≈38.72 years).

Conclusion: The correct answer is 38.72 years, matching the provided answer.

类似问题

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.

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.

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?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单