If Kai invests $4,500 today at 7% interest compounded quarterly, what will her account grow to after 20 years?

If Kai invests $4,500 today at 7% interest compounded quarterly, what will her account grow to after 20 years?

• A. $10,000
• B. $14,663
• C. $20,000
• D. $30,000

Answer: (B)

To find out how much Kai's investment will grow to after 20 years with an initial investment of $4,500 at an interest rate of 7% compounded quarterly, we can use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] 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. - \( t \) is the number of years the money is invested for. In this case: - \( P = 4,500 \) - \( r = 0.07 \) (which is 7% expressed as a decimal) - \( n = 4 \) (as the interest is compounded quarterly) - \( t = 20 \) Plugging in these values into the formula, we get: \[ A = 4500 \left(1 + \frac{0.07}{4}\right)^{4 \times 20} \]

To find out how much Kai's investment will grow to after 20 years with an initial investment of $4,500 at an interest rate of 7% compounded quarterly, we can use the compound interest formula:

[ A = P \left(1 + \frac{r}{n}\right)^{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.

• ( t ) is the number of years the money is invested for.

In this case:

• ( P = 4,500 )

• ( r = 0.07 ) (which is 7% expressed as a decimal)

• ( n = 4 ) (as the interest is compounded quarterly)

• ( t = 20 )

Plugging in these values into the formula, we get:

[ A = 4500 \left(1 + \frac{0.07}{4}\right)^{4 \times 20} ]