Final answer:
After calculating both compound and simple interest, the exact amount Robert gets after 2 years at an 8% interest rate does not match any of the provided answer choices. The calculated amount using compound interest is $3499.20, and using simple interest, without reinvestment, it is $3480.00, indicating a possible error in the provided options.
Step-by-step explanation:
The student wants to know the amount of money Robert gets after depositing $3000 in a bank account at an 8% annual interest rate for 2 years. To find the total amount after 2 years, we apply the formula for compound interest, A = P(1 + r/n)^(nt), where:
- P is the principal amount ($3000),
- r is the annual interest rate (8% or 0.08),
- n is the number of times interest is compounded per year (once, if not stated otherwise), and
- t is the number of years (2).
Using the given values, we get A = 3000(1 + 0.08/1)^(1*2) = 3000(1.08)^2 = 3000 * 1.1664 = $3499.20. However, none of the provided options match this figure, so there may have been a mistake. Since the options given seem to imply simple interest rather than compound interest, we'll calculate that instead: A = P(1 + rt) = 3000(1 + 0.08*2) = 3000(1 + 0.16) = 3000 * 1.16 = $3480. Again, no match. If we calculate only the interest earned over two years using simple interest, we get I = Prt = 3000 * 0.08 * 2 = $480. Adding this to the principal, we get 3000 + 480 = $3480, which is closer but still does not match any of the provided answers. However, if the interest earned is not reinvested, as in simple interest, the total amount Robert would have after 2 years by just adding the yearly interest to the principal would be the principal plus two years of interest which is $3000 + $240 + $240 = $3480, which still doesn't match any options but is closer. There seems to be an inconsistency in the question or its options.