A 10 10 -year government bond paid 5.8 % 5.8\% simple interest per year. Over the 10 10 years, the bond earned $ 4 , 640 \$4,640 in interest. What was the principal of the bond?

For this problem, a ten year government bond paid 5.8% simple interest per year. So over the ten years, the bond earned $4,640 in interest. What was the principal amount of the bond? So to solve this, we're gonna use our simple interest formula, I equals p r t. And let's figure out what values we already know so we can solve for what we don't know. Here, we know the amount of time is ten years. We also know that the rate is 5.8%, and we know the amount of interest earned was $4,640. And what we don't know is the principal amount of the bond. So let's plug in all those values that we already know. We'll have 4,640 is equal to our principal amount times our rate as a decimal is 0.058 times the amount of time, ten years. Simplifying, we get 4,640 is equal to p times 0.58. Next, we'll isolate by dividing both sides by 0.58. And we get that p is equal to 8,000. So the principal amount of money for the bond is $8,000.

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Multiple Choice

A $10$ -year government bond paid $5.8 percent sign$ simple interest per year. Over the $10$ years, the bond earned $dollar sign 4 comma 640$ in interest. What was the principal of the bond?

$dollar sign 3360$

$dollar sign 7000$

$dollar sign 8000$

\$80000

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Verified step by step guidance

Identify the formula for simple interest: $I = P \times r \times t$, where $I$ is the interest earned, $P$ is the principal, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Convert the given interest rate from a percentage to a decimal by dividing by 100: \$5.8\% = \frac{5.8}{100} = 0.058$.

Substitute the known values into the simple interest formula: \$4640 = P \times 0.058 \times 10$.

Simplify the right side of the equation by multiplying the interest rate and the time: \$4640 = P \times 0.58$.

Solve for the principal $P$ by dividing both sides of the equation by 0.58: $P = \frac{4640}{0.58}$.

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