Simple Interest Simple interest varies jointly as principal and time. If \$1000 invested for 2 yr earned \$70, find the amount of interest earned by \$5000 invested for 5 yr.

Verified step by step guidance

1. Identify the formula for simple interest that varies jointly as principal and time: \(I = k \times P \times T\), where \(I\) is the interest, \(P\) is the principal, \(T\) is the time, and \(k\) is the constant of proportionality.
2. Use the given information to find the constant \(k\). Substitute \(I = 70\), \(P = 1000\), and \(T = 2\) into the formula: \$70 = k \times 1000 \times 2$.
3. Solve for \(k\) by isolating it on one side: \(k = \frac{70}{1000 \times 2}\).
4. Use the value of \(k\) to find the interest earned for \(P = 5000\) and \(T = 5\). Substitute these values into the formula: \(I = k \times 5000 \times 5\).
5. Calculate the expression to find the interest earned for the new principal and time.

Key Concepts

Simple Interest Formula

Simple interest is calculated using the formula I = PRT, where I is the interest earned, P is the principal amount, R is the rate of interest per year, and T is the time in years. This formula shows how interest depends linearly on principal and time.

Joint Variation

Joint variation means a quantity varies directly as the product of two or more variables. In this problem, simple interest varies jointly as principal and time, implying I = kPT for some constant k, which can be found using given data.

Proportional Reasoning

Proportional reasoning involves comparing ratios to find unknown values. Once the constant of variation is found, you can set up a proportion to calculate the interest for different principal and time values by maintaining the same ratio.