Question

To help pay for a class trip at the end of their senior​ year, the sophomore class at a high school invests ​$1700 from​ fundraisers in a 30​-month CD paying 4.5​% interest compounded monthly. Determine the amount the class will receive when it crashes in the CD after 30 months.

Answer 1

Using the compound interest formula, the sophomore class would receive approximately $1901.93 from their $1700 investment in a 30-month CD at 4.5% interest compounded monthly after 30 months.

Step-by-step explanation:

To calculate the final amount obtained from a certificate of deposit (CD) with compounded interest, you can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

In this case, the high school sophomore class invested $1700 at an annual interest rate of 4.5% (0.045 in decimal form) compounded monthly (n = 12) for a period of 30 months (which is 30/12 = 2.5 years). Therefore, the formula to determine the amount they will receive after 30 months would be:

A = 1700 * (1 + 0.045/12)^(12*2.5)

Let's do the math:

A = 1700 * (1 + 0.00375)^(30)

A = 1700 * (1.00375)^30

A ≈ 1700 * 1.11878

A ≈ $1901.93

So, after 30 months, the sophomore class would receive approximately $1901.93 when they cash in their CD.

Answer 2

$1,902

Step-by-step explanation:

To calculate how much the class will receive we have to use the compound interest formula:

total amount = principal (1 + r)ⁿ

where:

principal = $1,700

r = 4.5% / 12 = 0.375% = 0.00375

n = 30 months

total amount = $1,700 (1 + 0.00375)³⁰ = $1,700 (1.118836) = $1,902