If an amount $AAA today earns interest at a rate of i percent per year, then the accumulated amount at the end of n years will be
A) $\$ A A A \times n \times i$
B) $\$ A A A \times i ^ { n }$
C) $( \$ A A A ) ^ { n } \times ( 1 + i )$
D) $\$ A A A \times ( 1 + i ) ^ { n }$

Question

Quizplus · Accepted Answer

The formula for compound interest is A=P(1+r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years. If we assume the interest is compounded annually (n=1), then the formula simplifies to A=P(1+r)^t. In this case, the principal is $AAA, the interest rate is i percent, and the time period is n years. Thus, the accumulated amount at the end of n years is $AAA(1+i)^n, which is equivalent to choice D.

If an Amount $AAA Today Earns Interest at a Rate $AAA×n×i\$ A A A \times n \times i$AAA×n×i

If an Amount $AAA Today Earns Interest at a Rate $\$ A A A \times n \times i$