Calculate the amount of interest earned in 9 years on $11,000 deposited in an account paying 10% annual interest, compounded quarterly. (Round your answer to the nearest cent.)
show your work
To calculate the amount of interest earned in 9 years on $11,000 deposited in an account paying 10% annual interest, compounded quarterly, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after time t
P = the principal amount (initial deposit) ($11,000)
r = annual interest rate (10% or 0.10)
n = number of times interest is compounded per year (4 for quarterly)
t = number of years (9)
Plugging in the values:
A = $11,000(1 + 0.10/4)^(4*9)
A = $11,000(1 + 0.025)^36
A = $11,000(1.025)^36
A = $11,000(1.758196)
A = $19,340.16
Total amount after 9 years = $19,340.16
Total interest earned = $19,340.16 - $11,000 = $8,340.16
Therefore, the amount of interest earned in 9 years on $11,000 deposited in an account paying 10% annual interest, compounded quarterly is $8,340.16.
no
To calculate the amount of interest earned on $11,000 deposited in an account paying 10% annual interest, compounded quarterly, for 9 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after time t
P = the principal amount ($11,000)
r = annual interest rate (10% or 0.10)
n = number of times interest is compounded per year (4 for quarterly)
t = number of years (9)
Plugging in the values:
A = $11,000(1 + 0.10/4)^(4*9)
A = $11,000(1 + 0.025)^36
A = $11,000(1.025)^36
A = $11,000(2.342726)
A = $25,770.99
Total amount after 9 years = $25,770.99
Total interest earned = $25,770.99 - $11,000 = $14,770.99
Therefore, the amount of interest earned in 9 years on $11,000 deposited in an account paying 10% annual interest, compounded quarterly is $14,770.99.
still no.
I apologize for the error in the previous calculations. Let's correct the calculation:
Given:
Principal amount (P) = $11,000
Annual interest rate (r) = 10% or 0.10
Number of compounding periods per year (n) = 4 (quarterly)
Number of years (t) = 9
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
A = $11,000(1 + 0.10/4)^(4*9)
A = $11,000(1 + 0.025)^36
A = $11,000(1.025)^36
A = $11,000(2.083375)
A = $22,916.13
Total amount after 9 years = $22,916.13
Interest earned = Total amount - Principal
Interest earned = $22,916.13 - $11,000
Interest earned = $11,916.13
Therefore, the amount of interest earned in 9 years on $11,000 deposited in an account paying 10% annual interest, compounded quarterly is $11,916.13.
The answer is 15,757.89. why
Apologies for the confusion in the previous calculations. Let's go through the correct calculation using the formula for compound interest:
Given:
Principal amount (P) = $11,000
Annual interest rate (r) = 10% or 0.10
Number of compounding periods per year (n) = 4 (quarterly)
Number of years (t) = 9
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
A = $11,000(1 + 0.10/4)^(4*9)
A = $11,000(1 + 0.025)^36
A = $11,000(1.025)^36
A = $11,000(2.349717)
A = $25,847.89
Total amount after 9 years = $25,847.89
Interest earned = Total amount - Principal
Interest earned = $25,847.89 - $11,000
Interest earned = $14,847.89
Therefore, the correct amount of interest earned in 9 years on $11,000 deposited in an account paying 10% annual interest, compounded quarterly is $14,847.89. Thank you for pointing out the error.