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.

Princip of Econ-Microeconomics Module 13 Practice Questions: Present & Future Value

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