Zaki invests \( \$ 500 \) 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 \( \$ 1,300 \). He then lets the account sit for 5 years. a. How much money does Zaki have after the first 2 years (before the deposit)? b. What is his new balance after depositing \( \$ 750 \) ? c. How much money does Zaki have in the account at the end of the next 3 years (before the next deposit)? d. What is his new balance after depositing \( \$ 1,300 \) ? e. How much money does Zaki have in the account at the end of the 10 year period? e. \( 50.51+6.055)^{2}=556.51 \) How much did Zaki earn in interest?

Let's tackle each part of Zaki's investment step by step. ### **Given:** - **Initial Investment:** \$500 - **Annual Interest Rate:** 5.5% - **Additional Deposits:** - **After 2 years:** \$750 - **After 5 years (3 years after the second deposit):** \$1,300 - **Total Investment Period:** 10 years Assuming the interest is **compounded annually**, let's proceed with each part. --- ### **a. Amount After the First 2 Years (Before the \$750 Deposit)** **Calculation:** \[ A = P(1 + r)^n \] Where: - \( P = \$500 \) - \( r = 5.5\% = 0.055 \) - \( n = 2 \) years \[ A = 500 \times (1 + 0.055)^2 = 500 \times 1.113025 = \$556.51 \] **Answer:** After the first 2 years, Zaki has **\$556.51** in the account. --- ### **b. New Balance After Depositing \$750** **Calculation:** \[ \text{New Balance} = \text{Previous Amount} + \text{Deposit} = 556.51 + 750 = \$1,306.51 \] **Answer:** After depositing \$750, the new balance is **\$1,306.51**. --- ### **c. Amount After the Next 3 Years (Before the \$1,300 Deposit)** **Calculation:** \[ A = P(1 + r)^n \] Where: - \( P = \$1,306.51 \) - \( r = 5.5\% = 0.055 \) - \( n = 3 \) years \[ A = 1,306.51 \times (1.055)^3 \approx 1,306.51 \times 1.17424 \approx \$1,534.14 \] **Answer:** At the end of the next 3 years, Zaki has **\$1,534.14** in the account. --- ### **d. New Balance After Depositing \$1,300** **Calculation:** \[ \text{New Balance} = \text{Previous Amount} + \text{Deposit} = 1,534.14 + 1,300 = \$2,834.14 \] **Answer:** After depositing \$1,300, the new balance is **\$2,834.14**. --- ### **e. Amount at the End of the 10-Year Period** **Calculation:** \[ A = P(1 + r)^n \] Where: - \( P = \$2,834.14 \) - \( r = 5.5\% = 0.055 \) - \( n = 5 \) years First, calculate \( (1.055)^5 \): \[ (1.055)^5 \approx 1.3064 \] Then, \[ A = 2,834.14 \times 1.3064 \approx \$3,702.61 \] **Answer:** At the end of 10 years, Zaki has **\$3,702.61** in the account. --- ### **f. Total Interest Earned** **Calculation:** \[ \text{Total Deposits} = 500 + 750 + 1,300 = \$2,550 \] \[ \text{Final Amount} = \$3,702.61 \] \[ \text{Interest Earned} = \text{Final Amount} - \text{Total Deposits} = 3,702.61 - 2,550 = \$1,152.61 \] **Answer:** Zaki earned **\$1,152.61** in interest over the 10-year period.