Multiple choice

Ingrid invested $20,000 in a heritage preservation bond offered by Aurora Capital, which paid simple interest at a rate of 6% per year. After a few years, she rolled over the entire maturity amount into a long-term sustainability fund at Solstice Group, where it earned simple interest at a rate of 7.5% per year for 8 years. The total interest earned from both investments was in the ratio 5 : 8. For how many years did Ingrid keep her funds with Aurora Capital?

  1. 4 years

  2. 6 years

  3. 8 years

  4. 10 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let t be the years at Aurora. Interest 1 = 20,000 * 0.06 * t = 1200t. Maturity amount = 20,000 + 1200t. Interest 2 = (20,000 + 1200t) * 0.075 * 8 = (20,000 + 1200t) * 0.6 = 12,000 + 720t. Ratio 1200t / (12,000 + 720t) = 5/8. Cross-multiplying: 9600t = 60,000 + 3600t, so 6000t = 60,000, t = 10.

AI explanation

The first interest is 20000 times 0.06 times x, which simplifies to 1200x. The second interest is the maturity amount (20000 plus 1200x) multiplied by 0.075 and by 8, simplifying to 12000 plus 450x. Given the ratio of these interests is 5 to 8, we solve the equation 1200x divided by (12000 plus 450x) equals 5 divided by 8. Cross-multiplying and solving for x yields a time period of 10 years.

Keep practicing — related questions