Calculate the future amounts you would have if $2,000 were invested at 8% for 4 years with simple interest and if it were invested with annual compounding. What is the difference between the two to the nearest cent, and does compound interest yield more or less than simple interest?
A) at simple interest, $2,640 with annual compounding, $2,721
Difference, $81 more;
B) at simple interest, $2,720.98 with annual compounding, $2,640
Difference, $80.98 more;
C) at simple interest, $2,720.98 with annual compounding, $2,640
Difference, $80.98 less;
D) at simple interest, $2,640 with annual compounding, $2,720.98
Difference, $80.98 less;
E) at simple interest, $2,640 with annual compounding, $2,720.98
Difference, $80.98 more;

Question

Quizplus · Accepted Answer

Simple interest is calculated as $P \times r \times t$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. For the given problem, $P = \$2,000$, $r = 0.08$, and $t = 4$. Thus, the future value with simple interest is $2000 \times 0.08 \times 4 = \$640$ in interest, plus the original \$2,000, for a total of \$2,640.For compound interest, the formula is $P(1 + r)^t$. Using the same values, the future value with annual compounding is $2000 \times (1 + 0.08)^4 \approx \$2,720.98$.The difference between the two methods is $\$2,720.98 - \$2,640 = \$80.98$, and compound interest yields more than simple interest.

Calculate the Future Amounts You Would Have If $2,000 Were