Jack has $1,000 that he wishes to invest for the next two years. One-year CDs are currently paying 8% while two-year CDs are paying 12% per annum. Economists are predicting that interest rates will rise by the end of the year. What is the minimum interest rates would have to increase to in order for the one-year CD to be better than the two-year CD?

Question

Quizplus · Accepted Answer

To determine the minimum interest rate increase required for the one-year CD to be a better investment than the two-year CD, we first calculate the total amount Jack would have after two years with each option. For the two-year CD at 12% per annum, the calculation is straightforward: $1,000 * (1 + 0.12)^2 = $1,254.40. For the one-year CD, we know the first year's interest rate is 8%, so the amount after one year is $1,000 * (1 + 0.08) = $1,080. For the one-year CD to be better, the interest rate in the second year (let's call it x) needs to result in a total greater than $1,254.40. The equation for the second year is $1,080 * (1 + x) > $1,254.40. Solving for x gives us x > 16.15%. Therefore, the interest rate would need to increase to more than 16% for the one-year CD to be a better option, making 16% the minimum increase required.

Jack Has $1,000 That He Wishes to Invest for the Next