Calculate the final loan amount of a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term.
$580.00
$583.20
$586.14
$86.14
To calculate the final loan amount, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final loan amount
P = the principal loan amount ($500.00)
r = the annual interest rate (16% or 0.16)
n = the number of compounding periods per year (12 since it's compounded monthly)
t = the number of years (1)
Using these values in the formula:
A = 500(1 + 0.16/12)^(12*1)
A ≈ 500(1 + 0.0133)^12
A ≈ 500(1.0133)^12
A ≈ 500(1.1709)
A ≈ $585.45
Rounding to the nearest cent, the final loan amount is $585.45. Therefore, the closest option is $586.14.
Calculate the interest amount of a $4,300 investment for a period of 20 years with a compound interest rate of 3.7% compounded quarterly.
$8,981.92
$4,681.92
$4,712.18
$4,702.27
To calculate the interest amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (Principal + Interest)
P = principal amount ($4,300)
r = the annual interest rate (3.7% or 0.037)
n = the number of compounding periods per year (4 since it's compounded quarterly)
t = the number of years (20)
Using these values in the formula:
A = 4300(1 + 0.037/4)^(4*20)
A ≈ 4300(1 + 0.00925)^(80)
A ≈ 4300(1.00925)^(80)
A ≈ 4300(2.208973822)
A ≈ $9,501.72
To find the interest amount, we need to subtract the principal ($4,300) from the final amount ($9,501.72):
Interest = $9,501.72 - $4,300
Interest = $5,201.72
Rounding to the nearest cent, the interest amount is $5,201.72. However, none of the provided options match this answer. Therefore, none of the options are correct.