Lucas is investing his tip eamings from the last 9 months of his waiter job in a savings account. Lucas has
in tip earnings saved up. The savings account earns simple interest. How much interest will
Lucas have at the end of 9 months? Round to the nearest cent.
What is the future value on Lucas’s account? Round to the nearest cent.

Question

Lucas is investing his tip eamings from the last 9 months of his waiter job in a savings account. Lucas has

in tip earnings saved up. The savings account earns

simple interest. How much interest will
Lucas have at the end of 9 months? Round to the nearest cent.
What is the future value on Lucas’s account? Round to the nearest cent.

UpStudy AI · Accepted Answer

Given:
  
- Principal $$ P = 6200 $$
- Annual simple interest rate $$ r = 2.7\% = 0.027 $$
- Time $$ t = 9 $$ months, which is $$ \frac{9}{12} = 0.75 $$ years

**Step 1. Calculate the interest earned**

The simple interest formula is:

$$
I = P \times r \times t
$$

Substitute the given values into the formula:

$$
I = 6200 \times 0.027 \times 0.75
$$

First, calculate $$ 6200 \times 0.027 $$:

$$
6200 \times 0.027 = 167.4
$$

Then multiply by $$ 0.75 $$:

$$
167.4 \times 0.75 = 125.55
$$

So, the interest earned is $$ I = 125.55 $$.

---

**Step 2. Calculate the future value of the account**

The future value $$ A $$ is the sum of the principal and the interest:

$$
A = P + I = 6200 + 125.55 = 6325.55
$$

---

**Final Answer:**

- Interest earned after 9 months: \$$$125.55$$
- Future value of Lucas's account: \$$$6325.55$$
Lucas will earn \$125.55 in interest over 9 months. The future value of his account will be \$6,325.55.

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