Question

$1500.00 is invested in anaccount with a 3% interest ratethat is compounded quarterly.How much money is in theaccount at the end of one year?A. $1,545.51B. $2,360.28C. $1,680.00D. $1,511.25

Answer 1

Using the compound interest formula, the future value of a $1500 investment with a 3% annual interest rate compounded quarterly after one year is approximately $1545.68. The closest answer provided is Option A ($1,545.51), which is likely the intended correct answer with rounding considerations.

Step-by-step explanation:

To determine the future value of a $1500 investment compounded quarterly at a 3% annual interest rate after one year, we use the compound interest formula:

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

Where:

• FV is the future value of the investment.
• P is the principal amount ($1500).
• r is the annual interest rate (3% or 0.03).
• n is the number of times interest is compounded per year (quarterly, so 4 times).
• t is the time the money is invested for, in years (1 year).

Plugging the numbers into the formula, we calculate:

FV = 1500(1 + 0.03/4)^(4*1)

FV = 1500(1 + 0.0075)^(4)

FV = 1500(1.0075)^4

FV = 1500 * 1.03045453395

FV = $1545.68

The correct answer is not listed in the provided options, but Option A is closest to the accurate calculation, therefore, Option A ($1,545.51) would likely be the intended answer when the question was created, allowing for possible rounding differences in the formula used.

Answer 2

We have the following data for an investment:

• A0 = initial amount of money ($) invested = 1500.00,

,

• r = interest rate in decimal = 3%/100% = 0.03,

,

• the interest is compounded quarterly.

Q) We want to know how much money will be in the account at the end of one year.

A) To calculate the amount of money after n years with an interest rate in decimal r, we can use the following formula:

`A(n)=A_0\cdot(1+(r)/(4))^(4n)`

Because we want to know the amount of money after one year, we must use n = 1. Replacing the data of our problem in the equation above we get:

`\begin{gathered} A(1)=1500\cdot(1+(0.03)/(4))^(4\cdot1) \\ A(1)=1500\cdot(1.0075)^4 \\ A(1)\cong1545.51 \end{gathered}`

Answer

A. $1,545.51