Assume a bank gives you an interest rate of 4% for putting $10,000 in an account for 40 years. How much money do you have in that account after 40 years?

Note: enter answer with only numerical values and round up to the nearest tenth. For example, if you think the answer is "$101.58" then enter the answer "101.6" in the space below.

Question

Assume a bank gives you an interest rate of 4% for putting $10,000 in an account for 40 years. How much money do you have in that account after 40 years?

Note: enter answer with only numerical values and round up to the nearest tenth. For example, if you think the answer is "$101.58" then enter the answer "101.6" in the space below.

BlackTom AI · Accepted Answer

We start with the basic formula for compound interest when the interest is compounded annually: A = P(1 + r)^t, where P is the principal, r is the annual interest rate (as a decimal), and t is the number of years.

- Given: P = 10,000, r = 0.04 (4%), t = 40 years.
- Compute the growth factor over 40 years: (1 + r)^t = (1.04)^{40}.
- Estimating (1.04)^{40} can be done by breaking it down: (1.04)^{10} ≈ 1.480244, then squaring to get (1.04)^{20} ≈ (1.480244)^2 ≈ 2.1907, and squaring again to obtain (1.04)^{40} ≈ (2.1907)^2 ≈ 4.801. This emphasizes the substantial growth over four decades.
- Apply the growth factor to the principal: A ≈ 10,000 × 4.801 ≈ 48,010.

To align with the instruction of rounding to the nearest tenth, we refine the estimate: (1.04)^{40} is approximately 4.8010… which leads to A ≈ 10,000 × 4.8010… ≈ 48,010.0. If more precise computation is performed, the value rounds to about 48,010.2 dollars when carried to one decimal place.

Summary steps in plain terms: multiply the initial amount by the factor by which money grows at 4% per year for 40 years, then round the result to one decimal place. The essential idea is applying A = P(1 + r)^t and then performing the rounding as specified.

Note: If you were to present the final amount strictly as a numerical value with one decimal place, you would enter 48010.2 in the answer box.

类似问题

Part 1Consider a twominus−year investment: Given a constant and positive interest rate, the interest earned in the second year will be greater than the interest earned in the first year (assuming annual compounding). Part 1 True False

If Jack and Jill deposit $1,000 into a savings account that earns 4.5% annual interest (compounded monthly), how long will it take for their money to double to $2,000?

How much will you get back on a five year investment of $100 that pays 5% interest per year?

What is the effective yield (APY) if the Annual Percentage Rate (APR) is 7.64 percent and it is compounded quarterly?

If you deposit $10,000 in an account with an annual rate of 9% compounded semiannually, how long will it take for you to have $2,000,000 in the account?

In order to determine the future value of some lump sum, we must use the process of ________.

With compound interest, the investor earns interest on the principal amount invested plus interest on accumulated interest. Which of the following compounding frequencies would yield the investor the greatest ending balance assuming all else is equal?

You have located an investment that pays 9 percent per year. You invest $800. How much will you have in seven years? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.Blank.xlsx

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