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?

Question

UpStudy AI · Accepted Answer

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.
After 10 years, Zaki has \$3,702.61 in the account and earned \$1,152.61 in interest.

Solución de inteligencia artificial de Upstudy

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Solución

Given:

a. Amount After the First 2 Years (Before the $750 Deposit)

b. New Balance After Depositing $750

c. Amount After the Next 3 Years (Before the $1,300 Deposit)

d. New Balance After Depositing $1,300

e. Amount at the End of the 10-Year Period

f. Total Interest Earned

Mind Expander

a. After the first 2 years (before new deposit):

b. After depositing $750:

c. At the end of the next 3 years (before new deposit):

d. After depositing $1,300:

e. At the end of the 5-year period:

f. Total interest earned:

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