Problem

Suppose that $2000 is invested at a rate of 3.1%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 5 years.
Do not round any intermediate computations, and round your answer to the nearest cent.

Answer

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Answer

Round the final result to the nearest cent: 2332.54

Steps

Step 1 :Given that the principal amount (P) is $2000, the annual interest rate (r) is 3.1% or 0.031 in decimal, the number of times that interest is compounded per year (n) is 2 (since it's compounded semiannually), and the time the money is invested for in years (t) is 5 years.

Step 2 :We can use the formula for compound interest to find the total amount (A) after 5 years. The formula is A=P(1+rn)nt

Step 3 :Substitute the given values into the formula: A=2000(1+0.0312)25

Step 4 :Calculate the value inside the parentheses: 1+0.0312=1.0155

Step 5 :Raise the result to the power of 10 (2 times 5 years): (1.0155)10=1.1662704646057548

Step 6 :Multiply the result by the principal amount: 20001.1662704646057548=2332.5409292115096

Step 7 :Round the final result to the nearest cent: 2332.54

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