22. A certificate of deposit (CD) is a savings contract that requires you to leave your money "locked in" the account for a certain amount of time in exchange for a higher interest rate. For each of the CDs described, determine the account balance at the end of the contract if you have an initial deposit of \( \$ 1,000 \) and the interest is compounded monthly. a. \( 2 \% \) annual interest rate; for 3 years b. \( 2 \% \) annual interest rate; for 5 years (1 point) c. \( 3 \% \) annual interest rate; for 5 years 23. Based your model, do you think it is worth it to have your money locked into a CD in order to a higher interest rate? Explain. d. \( 3 \% \) annual interest rate; for 7 years (1 point) (1 points) (1 point) (1)

We’ll use the compound‐interest formula   A = P · (1 + r/m)^(m·t) where   • P = initial deposit ($1,000),   • r = annual interest rate (as a decimal),   • m = number of compounding periods per year (12 for monthly compounding),   • t = number of years. ────────────────────────────── a. 2% annual for 3 years Here: r = 0.02, m = 12, t = 3.   A = 1000 · (1 + 0.02/12)^(12×3)     = 1000 · (1 + 0.00166667)^(36)     ≈ 1000 · (1.06168)     ≈ $1,061.68 ────────────────────────────── b. 2% annual for 5 years Here: r = 0.02, m = 12, t = 5.   A = 1000 · (1 + 0.02/12)^(12×5)     = 1000 · (1.00166667)^(60)     ≈ 1000 · (1.10517)     ≈ $1,105.17 ────────────────────────────── c. 3% annual for 5 years Here: r = 0.03, m = 12, t = 5.   Monthly rate = 0.03/12 = 0.0025.   A = 1000 · (1 + 0.0025)^(12×5)     = 1000 · (1.0025)^(60)     ≈ 1000 · (1.16162)     ≈ $1,161.62 ────────────────────────────── d. 3% annual for 7 years Here: r = 0.03, m = 12, t = 7.   A = 1000 · (1 + 0.03/12)^(12×7)     = 1000 · (1.0025)^(84)     ≈ 1000 · (1.23385)     ≈ $1,233.85 ────────────────────────────── 23. Is It Worth Locking Your Money into a CD for a Higher Interest Rate? Whether or not a CD is “worth it” depends on your financial needs and market conditions: • Pros:   ◦ CDs offer a guaranteed return once you commit to the term.   ◦ Because the interest compounds monthly, you get a steady growth of your savings.   ◦ In a low‐interest-rate environment, the slightly higher rate on a CD might be attractive if you know you won’t need the money. • Cons:   ◦ Your money is locked in for the term of the CD, meaning you cannot access it without potentially incurring penalties.   ◦ If interest rates rise during your CD’s term, you might miss out on better yields available elsewhere.   ◦ The incremental gain might be relatively modest. For example, with a $1,000 deposit, the difference between a 2% rate and a 3% rate over several years only accounts for tens to a couple hundred dollars. In conclusion, if you are sure you don’t need the funds soon and you value a secure, predictable return, locking your money in a CD can be worthwhile. On the other hand, if you value liquidity or if there’s a possibility that rates will rise further soon, you might prefer an account that offers easier access to your funds. The decision depends on your personal financial situation and market expectations.