Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A financial advisor is explaining compound interest. An initial investment of $8,000 earns an annual interest rate of 4%, compounded quarterly. If no additional deposits or withdrawals are made, what will be the value of the investment after 2 years?
- A$8,675.29
- B$8,653.00
- C$8,666.19
- D$8,664.88
Show answer & explanationAnswer & explanation
Correct answer: D. $8,664.88
Use the compound interest formula A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate, n is the number of times interest is compounded per year, and t is the number of years.
Why the other options are wrong
- A. This is incorrect; potentially a calculation error or using annual compounding instead of quarterly.
- B. This is incorrect; likely an error in calculation or using the wrong number of compounding periods.
- C. This is incorrect; perhaps a slight rounding error or miscalculation.
Compound Interest (General)
Compound interest is interest calculated on the initial principal and also on the accumulated interest from previous periods. The more frequently interest is compounded, the faster the investment grows.
- Formula: A = P(1 + r/n)^(nt)
- P = principal, r = annual interest rate, n = compounding periods per year, t = time in years.
- Used for investments, loans, and financial growth.
Memory trick: Principal times (one plus rate over periods) to the power of (periods times years), that's the wealth it clears!