A retirement fund invests some money in government bonds at $2.5\%$ annual simple interest, and \(5,000 more than that amount in corporate bonds at $4\%$. If the total annual interest earned is $\mathrm{\backslash )}1,450$, how much was invested in each type of bond?

• A. Government bonds = \(24,230.77; Corporate bonds = \)19,230.77
• B. Government bonds = \(19,230.77; Corporate bonds = \)24,230.77
• C. Government bonds = \(18,500.50; Corporate bonds = \)23,500.50
• D. Government bonds = \(23,500.50; Corporate bonds = \)18,500.50

Answer: (B)

Verified step by step guidance

1. Let the amount invested in government bonds be \(x\). According to the problem, the amount invested in corporate bonds is \(x + 5000\).
2. Write expressions for the annual interest earned from each type of bond using simple interest formula: Interest = Principal \(\times\) Rate. For government bonds, the interest is \(0.025 \times x\), and for corporate bonds, it is \(0.04 \times (x + 5000)\).
3. Set up an equation for the total interest earned by adding the two interest amounts and equating to the total interest given: \(0.025x + 0.04(x + 5000) = 1450\).
4. Simplify the equation by distributing and combining like terms: \(0.025x + 0.04x + 0.04 \times 5000 = 1450\).
5. Solve the resulting linear equation for \(x\) to find the amount invested in government bonds, then add 5000 to find the amount invested in corporate bonds.