Question

you invest $15,000 at an annual rate of 8.25or one year. what is the difference in interest earned if your investment is compounded on a monthly basis instead of an annual basis?

Answer 1

The difference in interest earned if your investment is compounded on a monthly basis instead of an annual basis is $1185

"8.25% interest" denotes an interest rate of 8.25% yearly, compounded. "8.25% interest compounded monthly" refers to the annual interest rate, which is 8.25% and is compounded every month. The interest rate is, therefore (8.25%) / (12) = 0.6875% monthly. It is clear what is meant by "0.6875% interest per month compounded monthly." Problems must be resolved in terms of the compounding period rather than years when the compounding period is not annual.

P = 15000, r = 0.0825 (8.25%), n = 12 , and t = 1 (given)

Using the formula for monthly compound interest,

$CI = P (1 +\frac{r}{n})^{nt} - P$

CI = 15000 [1 + (0.0825 / 12)] ¹² - 15000

CI = (15000 * 1.086) - 15000

CI = 16290 - 15000

CI = 1290

Therefore, Compound Interest when compounded on monthly basis will be $1290.

Annual Compound Interest:

$CI = P (1 +\frac{r}{n})^{nt} - P$

CI =  15000 [1 + (0.0825 / 12)] ¹ - 15000

CI = (15000 * 1.007) - 15000

CI = 15105 - 15000

CI = $105

Therefore, Compound Interest when compounded annually will be $105.

The difference in interest earned  if the investment is compounded monthly instead of annual basis will be

Difference = $1290 - $105 = $1185

To know more about Compound Interest, refer to this link:

brainly.com/question/20406888

#SPJ4