### Instruction: An investment of $\$$10,000 is made in a government bond that will pay 6$\%$ interest compounded annually. At the end of five years, what is the total number of dollars in this investment? Express your answer to the nearest whole number.### Response: To find the total amount in the investment after five years, I need to use the formula for compound interest: A = P(1 + r)^n, where A is the final amount, P is the principal, r is the interest rate per period, and n is the number of periods.
In this problem, P is 10,000, r is 0.06, and n is 5, since the interest is compounded annually and the bond has a term of five years.
Plugging these values into the formula, I get A = 10,000(1 + 0.06)^5.
Using a calculator, I can simplify the expression inside the parentheses: 1 + 0.06 = 1.06.
Then, I can raise 1.06 to the fifth power: 1.06^5 = 1.33823, rounded to five decimal places.
Multiplying by 10,000, I get A = 13,382.26, rounded to two decimal places.
The problem asks for the answer to the nearest whole number, so I need to round 13,382.26 to the closest integer.