If 7000 dollars is invested in a bank account at an interest rate of 7 per cent per year.
A) Find the amount in the bank after 6 years if interest is compounded annually?
B) Find the amount in the bank after 6 years if interest is compounded quaterly?
C) Find the amount in the bank after 6 years if interest is compounded monthly?
D) Finally, find the amount in the bank after 6 years if interest is compounded continuously?
A=?
B=?
C=?
D=?
Thanks again guys!
$4000 is invested at 9% compounded quarterly. In how many years will the account have grown to $14,500? Round your answer to the nearest tenth of a year
deg
To find the amount in the bank after a certain period of time with different compounding frequencies, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment) = $7000
r = annual interest rate (in decimal form) = 0.07
n = the number of times that interest is compounded per year
t = the number of years
Now, let's calculate the amounts for each case:
A) Compounded Annually (n = 1)
Using the formula:
A = 7000(1 + 0.07/1)^(1*6)
A = 7000(1.07)^6
A ≈ $10,931.47
So, the amount in the bank after 6 years with annual compounding is approximately $10,931.47.
B) Compounded Quarterly (n = 4)
Using the formula:
A = 7000(1 + 0.07/4)^(4*6)
A = 7000(1.0175)^24
A ≈ $11,005.07
Therefore, the amount in the bank after 6 years with quarterly compounding is approximately $11,005.07.
C) Compounded Monthly (n = 12)
Using the formula:
A = 7000(1 + 0.07/12)^(12*6)
A ≈ $11,039.88
The amount in the bank after 6 years with monthly compounding is approximately $11,039.88.
D) Compounded Continuously
Using the formula:
A = P*e^(rt)
A = 7000*e^(0.07*6)
A ≈ $11,051.27
The amount in the bank after 6 years with continuous compounding is approximately $11,051.27.
So, the answers are:
A) $10,931.47
B) $11,005.07
C) $11,039.88
D) $11,051.27
B)
compounded quarterly
----> i = .07/4 or .0175, and n = 6(4) or 24
amount = 7000(1.0175)^24
= $ 10,615.10
Do A and C the same way
D
amount = 7000 e^(6(.07))
= $ 10,653.73