score on last try: 1 of 4 pts. see details for more.\nat least one scored part is incorrect. jump to first…

score on last try: 1 of 4 pts. see details for more.\nat least one scored part is incorrect. jump to first changable incorrect part.\n> next question get a similar question you can retry this question below\n$3000 are invested in a bank account at an interest rate of 9 percent per year.\nfind the amount in the bank after 8 years if interest is compounded annually.\n5977.68\nfind the amount in the bank after 8 years if interest is compounded quarterly.\n6091.13\nfind the amount in the bank after 8 years if interest is compounded monthly.\n6115.14\nfinally, find the amount in the bank after 8 years if interest is compounded continuously.\n6163.30\nquestion help: video message instructor

score on last try: 1 of 4 pts. see details for more.\nat least one scored part is incorrect. jump to first changable incorrect part.\n> next question get a similar question you can retry this question below\n$3000 are invested in a bank account at an interest rate of 9 percent per year.\nfind the amount in the bank after 8 years if interest is compounded annually.\n5977.68\nfind the amount in the bank after 8 years if interest is compounded quarterly.\n6091.13\nfind the amount in the bank after 8 years if interest is compounded monthly.\n6115.14\nfinally, find the amount in the bank after 8 years if interest is compounded continuously.\n6163.30\nquestion help: video message instructor

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (P) is the principal amount ((P = 3000)), (r) is the annual interest rate (as a decimal, (r=0.09)), (t) is the number of years ((t = 8)), and (n) is the number of times interest is compounded per year.

Step2: Calculate for annual compounding ((n = 1))

Substitute (P = 3000), (r=0.09), (t = 8), (n = 1) into the formula: (A=3000(1 +\frac{0.09}{1})^{1\times8}=3000(1.09)^{8}) ((1.09)^{8}\approx1.99256) (A = 3000\times1.99256=5977.68)

Step3: Calculate for quarterly compounding ((n = 4))

Substitute (P = 3000), (r = 0.09), (t = 8), (n = 4) into the formula: (A=3000(1+\frac{0.09}{4})^{4\times8}=3000(1 + 0.0225)^{32}) ((1.0225)^{32}\approx2.03044) (A=3000\times2.03044 = 6091.32\approx6091.32)

Step4: Calculate for monthly compounding ((n = 12))

Substitute (P = 3000), (r=0.09), (t = 8), (n = 12) into the formula: (A=3000(1+\frac{0.09}{12})^{12\times8}=3000(1+\frac{0.0075})^{96}) ((1.0075)^{96}\approx2.03878) (A=3000\times2.03878=6116.34)

Step5: Recall continuous - compounding formula

The continuous - compounding formula is (A=Pe^{rt}), where (P = 3000), (r = 0.09), (t = 8) (A=3000e^{0.09\times8}=3000e^{0.72}) (e^{0.72}\approx2.05443) (A=3000\times2.05443 = 6163.29\approx6163.30)

Answer:

The amount for annual compounding is (5977.68), for quarterly compounding is (6091.32), for monthly compounding is (6116.34), and for continuous compounding is (6163.30)