Question

Tessa has recently inherited $5600, which she wants to deposit into a CD account. She has determined that her two best bets are an account that compounds monthly at an annual rate of 4.7 % (Account 1) and an account that compounds semi-annually at an annual rate of 5.1 % (Account 2)

a. How much would Tessa's balance be from Account 2 over 3.8 years?

Answer 1

To find Tessa's balance from Account 2 after 3.8 years, with an annual interest rate of 5.1% compounded semi-annually, we use the compound interest formula, resulting in the future value of her CD account.

Step-by-step explanation:

To calculate how much Tessa's balance would be from Account 2 over 3.8 years, we need to use the formula for compound interest which is 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 (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.

In Tessa's case with Account 2, which compounds semi-annually at an annual rate of 5.1%, the variables are:

• P = $5600
• r = 5.1/100 = 0.051
• n = 2 (because interest is compounded semi-annually)
• t = 3.8 years

Using the formula, A = 5600(1 + 0.051/2)^(2*3.8), we compute the value of Tessa's CD account after 3.8 years. To calculate the balance from Account 2 over 3.8 years, we can use the formula:

Balance = Principal * (1 + r/n)^(n*t)

Where:

Principal = $5600

r = annual interest rate (5.1%)

n = number of times interest is compounded per year (2)

t = time in years (3.8)

Plugging these values into the formula, we get:

Balance = $5600 * (1 + 0.051/2)^(2*3.8)

Balance ≈ $5600 * (1.0255)^(7.6)

Balance ≈ $5600 * 1.10528

Balance ≈ $6197.568

Therefore, Tessa's balance from Account 2 over 3.8 years would be approximately $6197.57.

Answer 2

Tessa's balance in Account 2, which compounds semi-annually at a 5.1% annual rate over 3.8 years, would be $6803.10.

Step-by-step explanation:

Calculating the Future Value of a CD Account

To calculate the future value of Tessa's investment in Account 2, which compounds semi-annually at an annual rate of 5.1%, we use the formula for compound interest:

FV = P(1 + r/n)^(nt), where:

• FV is the future value of the investment,
• P is the principal amount ($5600),
• r is the annual interest rate (0.051),
• n is the number of times the interest is compounded per year (2 for semi-annually),
• t is the time the money is invested for, in years (3.8).

First, we calculate the compound interest rate per period: (1 + 0.051/2).

Then, we calculate the number of periods by multiplying the number of years by the compounding frequency: 3.8 * 2.

Finally, we calculate Tessa's balance after 3.8 years by substituting these values into the formula: FV = 5600 * (1 + 0.051/2)^(2 * 3.8).

Performing the calculation results in a future value of $6803.10

Therefore, Tessa's balance in Account 2 over 3.8 years would be $6803.10.