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 = 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 = 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
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