Question

Santos deposited $1,800 in an account that yields 2.1% interest, compounded semi-annually. How much is in the account after 54 months? Round to the nearest cent.
a. $1,971.63
b. $1,825.34
c. $1,954.22
d. $1,890.09

Answer 1

Answer:

a. $1,971.63

Step-by-step explanation:

We can use the formula for compound interest:

A = P$(1+\frac{r}{n}) ^{(n)(t)}$

Where:

A = the final amount

P = the principal amount

r = the annual interest rate

n = the number of times interest is compounded per year

t = the time in years

We take

A = 1800$(1+\frac{0.021}{2}) ^{(2)(4.5)}$

A ≈ $1,971.63

So, the answer is a. $1,971.63.

Answer 2

Final answer:

To calculate the amount in the account after 54 months with 2.1% interest compounded semi-annually, use the formula A = P(1 + r/n)^(nt). Plug in the values and calculate A ≈ $1,971.63. The correct option is A .

Explanation:

To calculate the amount in the account after 54 months, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount in the account
• P is the principal amount (initial deposit)
• r is the annual interest rate (as a decimal)
• n is the number of times interest is compounded per year
• t is the time in years

In this case, P = $1,800, r = 2.1% = 0.021, n = 2 (compounded semi-annually), and t = 54 months / 12 = 4.5 years.

Plugging these values into the formula:

A = $1,800(1 + 0.021/2)^(2*4.5)

Simplifying the expression inside the parentheses:

A = $1,800(1.0105)^(9)

Evaluating the expression raised to the power of 9:

A ≈ $1,971.63

Therefore, the amount in the account after 54 months is approximately $1,971.63.