Question

$440 is invested in an account earning 6.6% interest (APR), compounded quarterly. Write a function showing the value of the account after

t
t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Answer 1

Rounding to the nearest hundredth of a percent, the APY is 6.8%.

Explanation:

A = P * (1 + r/n)^(n*t)

Where:

A = the value of the account after t years

P = the principal amount invested (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is invested

For this problem, we have P = $440, r = 0.066 (6.6% APR), n = 4 (compounded quarterly), and we want to find A after t years. Therefore, the function for the value of the account after t years is:

A(t) = 440 * (1 + 0.066/4)^(4t)

= 440 * (1.0165)^(4t)

= 440 * (1.0165^(4t))

Rounding to four decimal places, the function is:

A(t) = 440 * 1.0165^(4t)

To find the annual percentage yield (APY), we use the formula:

APY = (1 + r/n)^n - 1

Where:

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

For this problem, we have r = 0.066 (6.6% APR) and n = 4 (compounded quarterly). Therefore, the APY is:

APY = (1 + 0.066/4)^4 - 1

= 0.068

= 6.8%

Rounding to the nearest hundredth of a percent, the APY is 6.8%.