Question

$6,700 is invested in an account earning 8. 3% interest (APR), compounded daily. Write a function showing the value of the account after 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

A = $6,700(1 +0.0865^t)

APY = 8.65%

Explanation:

Daily compounding of interest results in an annual growth factor of ...

gf = (1 +r/365)^365 . . . . for APR = r

Your growth factor is ...

gf = (1 +0.083/365)^365 ≈ 1.086532

Then the growth rate (APY) is ...

APY = gf -1 ≈ 8.65%

The account value is multiplied by the growth factor each year, so after t years will be ...

A = P(1 +APY)^t

A = $6,700(1 +0.0865)^t . . . . . . . 0.0865 is the annual growth rate