On Your Oun Practice \[ A=P(1+r)^{+} \] 1. Yadiel invested 53.400 in a savings account that pays \( 6.2 \% \) interest compounded annually. Find the value of the investment in 9 years. \[ \begin{array}{l} \text { I invested } 53,400 \text { in a savings decs. } \\ 3,400=(1+0.062)=5842.51 \\ \text { lue of the investment in } 9 \text { years. } \end{array} \] Find the amount of interest Yadiel earned from this account. \[ \begin{array}{l} \text { d the amount of interest Yadiel earned from tnis } \\ 5842.81-3400=2442.51 \end{array} \] 2. Lify invested 55.000 in a savings account that pays \( 2.3 \% \) interest annually. Find the value of the investment in 4 years. \[ 4=5476.11 \] Find the amount of interest Lily earned from this account. \[ 47611 \] 3. Zati invests 5500 into a money market account that pays him \( 5.5 \% \) interest on his investment annually. After 2 years, Zaki puts an additional \( \$ 750 \) in the account. 3 years after that, he deposits another 51,300 . He then lets the account sit for 5 years. 2. How much money does Zaki have after the first 2 years (before the deposit)? \[ 500(1+0.055)^{2}=556.51 \] b. What is his new balance after depositing \( \$ 750 \) ? \[ 1206.81 \] c. How moch money does Zaki have in the account at the end of the next 3 years (before the next depositj? \[ 5 \] d. What is his new balance after depositing \( \$ 1,300 \) ? \[ 2834.16 \] e. Hons moch money does Zaki have in the account at the end of the 10 year period? 12 \( f \). How moch did Zaki earn in interest?

Certainly! Let's tackle each of these compound interest problems step by step to ensure clarity and accuracy. We'll address each question and its subparts systematically. --- ## **1. Yadiel's Investment** **Given:** - **Principal (P):** \$53,400 - **Annual Interest Rate (r):** 6.2% or 0.062 - **Time (n):** 9 years - **Compounding Frequency:** Annually ### **a. Calculate the Future Value of the Investment** The formula for compound interest compounded annually is: \[ A = P(1 + r)^n \] Plugging in the values: \[ A = 53,400 \times (1 + 0.062)^9 \] \[ A = 53,400 \times (1.062)^9 \] First, calculate \(1.062^9\): \[ 1.062^9 \approx 1.062^9 \approx 1.698 \] Now, multiply by the principal: \[ A \approx 53,400 \times 1.698 \approx 90,783.20 \] **Future Value (A):** **\$90,783.20** ### **b. Calculate the Amount of Interest Earned** \[ \text{Interest} = A - P = 90,783.20 - 53,400 = 37,383.20 \] **Interest Earned:** **\$37,383.20** --- ## **2. Lily's Investment** **Given:** - **Principal (P):** \$55,000 - **Annual Interest Rate (r):** 2.3% or 0.023 - **Time (n):** 4 years - **Compounding Frequency:** Annually ### **a. Calculate the Future Value of the Investment** \[ A = 55,000 \times (1 + 0.023)^4 \] \[ A = 55,000 \times (1.023)^4 \] First, calculate \(1.023^4\): \[ 1.023^4 \approx 1.023 \times 1.023 \times 1.023 \times 1.023 \approx 1.095 \] Now, multiply by the principal: \[ A \approx 55,000 \times 1.095 \approx 60,225 \] **Future Value (A):** **\$60,225** ### **b. Calculate the Amount of Interest Earned** \[ \text{Interest} = A - P = 60,225 - 55,000 = 5,225 \] **Interest Earned:** **\$5,225** --- ## **3. Zati's Investment Journey** **Given:** - **Initial Principal (P₁):** \$5,500 - **Annual Interest Rate (r):** 5.5% or 0.055 - **Deposits:** - **After 2 years:** \$750 - **3 years after the first deposit (total of 5 years from start):** \$1,300 - **Total Investment Period:** 10 years - **Compounding Frequency:** Annually We'll break this down step by step. ### **a. Amount After the First 2 Years (Before the First Deposit)** \[ A_2 = P₁ \times (1 + r)^n = 5,500 \times (1 + 0.055)^2 \] \[ A_2 = 5,500 \times (1.055)^2 = 5,500 \times 1.113025 \approx 6,121.64 \] **Amount After 2 Years:** **\$6,121.64** ### **b. New Balance After Depositing \$750** \[ \text{New Principal} = A_2 + 750 = 6,121.64 + 750 = 6,871.64 \] **New Balance:** **\$6,871.64** ### **c. Amount After the Next 3 Years (Before the Second Deposit)** Now, we apply compound interest for 3 more years on the new principal. \[ A_5 = 6,871.64 \times (1 + 0.055)^3 \] \[ A_5 = 6,871.64 \times (1.055)^3 = 6,871.64 \times 1.174618 \approx 8,070.63 \] **Amount After 5 Years:** **\$8,070.63** ### **d. New Balance After Depositing \$1,300** \[ \text{New Principal} = A_5 + 1,300 = 8,070.63 + 1,300 = 9,370.63 \] **New Balance:** **\$9,370.63** ### **e. Amount After the Next 5 Years (End of 10-Year Period)** \[ A_{10} = 9,370.63 \times (1 + 0.055)^5 \] \[ A_{10} = 9,370.63 \times (1.055)^5 = 9,370.63 \times 1.305506 \approx 12,213.95 \] **Final Amount After 10 Years:** **\$12,213.95** ### **f. Total Interest Earned** \[ \text{Total Interest} = A_{10} - (\text{Initial Principal} + \text{Deposits}) \] Initial Principal: \$5,500 First Deposit: \$750 Second Deposit: \$1,300 Total Deposits: \$5,500 + \$750 + \$1,300 = \$7,550 \[ \text{Interest} = 12,213.95 - 7,550 = 4,663.95 \] **Total Interest Earned:** **\$4,663.95** --- ## **Summary of Results** 1. **Yadiel's Investment:** - **Future Value:** \$90,783.20 - **Interest Earned:** \$37,383.20 2. **Lily's Investment:** - **Future Value:** \$60,225 - **Interest Earned:** \$5,225 3. **Zati's Investment:** - **Final Amount After 10 Years:** \$12,213.95 - **Total Interest Earned:** \$4,663.95 --- **Note:** It's essential to ensure that all calculations, especially exponents, are accurate. Using a calculator or spreadsheet software can help verify these results. Additionally, always double-check for any typographical errors in the initial data to ensure precise calculations.