Final answer:
a. After 9 years with annual compounding, the amount in the bank will be approximately $9858.25. b. After 9 years with quarterly compounding, the amount in the bank will be approximately $10060.41. c. After 9 years with monthly compounding, the amount in the bank will be approximately $10071.88. d. After 9 years with continuous compounding, the amount in the bank will be approximately $10084.72.
Step-by-step explanation:
a. To find the amount in the bank after 9 years with annual compounding, we can use the formula:
A = P(1 + r/n)^(nt)
where A is the amount in the bank, P is the initial investment, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Using the given values, we have:
A = 7000(1 + 0.04/1)^(1*9) = 7000(1.04)^9 ≈ $9858.25
b. To find the amount in the bank after 9 years with quarterly compounding, we use the same formula with n = 4:
A = 7000(1 + 0.04/4)^(4*9) = 7000(1.01)^36 ≈ $10060.41
c. To find the amount in the bank after 9 years with monthly compounding, we use the same formula with n = 12:
A = 7000(1 + 0.04/12)^(12*9) = 7000(1.003333)^108 ≈ $10071.88
d. To find the amount in the bank after 9 years with continuous compounding, we use the formula:
A = Pe^(rt)
where e is the base of the natural logarithm. Using the given values, we have:
A = 7000e^(0.04*9) ≈ $10084.72