Questions: A recent high school graduate received 600 in gifts of cash from friends and relatives. In addition, she received three scholarships in the amounts of 450, 500, and 1500. If she takes all her gift and scholarship money and invests it in a 24-month CD paying 1% interest compounded daily, how much will the graduate have when she cashes in the CD at the end of the 24-months? The graduate will have when she cashes in the CD. (Round to the nearest cent as needed.)

A recent high school graduate received 600 in gifts of cash from friends and relatives. In addition, she received three scholarships in the amounts of 450, 500, and 1500. If she takes all her gift and scholarship money and invests it in a 24-month CD paying 1% interest compounded daily, how much will the graduate have when she cashes in the CD at the end of the 24-months? The graduate will have when she cashes in the CD. (Round to the nearest cent as needed.)
Transcript text: A recent high school graduate received $\$ 600$ in gifts of cash from friends and relatives. In addition, she recerved three scholarships in the amounts of $\$ 450, \$ 500$, and $\$ 1500$. If she takes all her gift and scholarship money and invests it in a 24 -month CD paying $1 \%$ interest compounded daily, how much will the graduate have when she cashes in the $C D$ at the end of the 24 -months? The graduate will have $\$$ $\square$ when she cashes in the $C D$. (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Total Initial Investment

The total initial investment (P) is the sum of the fixed amount received as gifts ($600) and the amounts received from scholarships ($450, $500, $1500), which totals to $3050.

Step 2: Convert the Annual Interest Rate to a Decimal

The annual interest rate (1%) is converted to a decimal by dividing by 100, resulting in 0.01.

Step 3: Calculate the Future Value of the Investment

Using the formula \(A = P(1 + \frac{r}{n})^{nt}\), where \(P = $3050\), \(r = 0.01\), \(n = 365\) (daily compounding), and \(t = 2\) years, we calculate the future value of the investment.

Step 4: Round the Result

The future value of the investment, rounded to 2 decimal places, is $3111.61.

Final Answer:

The future value of the investment after 2 years, with an initial investment of $3050, an annual interest rate of 1%, compounded daily, is $3111.61.

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