Calculate the final loan amount of a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term. (1 point)
$583.20
• $86.14
• $580.00
$586.14
To calculate the final loan amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final loan amount
P = principal loan amount ($500)
r = annual interest rate (16% or 0.16)
n = number of times interest is compounded per year (12 for monthly)
t = number of years (1)
Substituting the given values into the formula:
A = 500(1 + 0.16/12)^(12*1)
A = 500(1 + 0.0133)^12
A = 500(1.0133)^12
A ≈ 500(1.169866)
A ≈ 584.93
Rounding to the nearest cent, the final loan amount is approximately $584.93. However, the answer choices are given in dollar amounts without decimal places. Therefore, the closest option is $583.20.
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. (1 point)
O $8,981.92
• $4,712.18
• $4,681.92
• $4,702.27
To calculate the interest amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = final amount (including interest)
P = principal amount ($4,300)
r = annual interest rate (3.7% or 0.037)
n = number of times interest is compounded per year (4 for quarterly)
t = number of years (20)
Substituting the given values into the formula:
A = 4300(1 + 0.037/4)^(4*20) - 4300
A = 4300(1 + 0.00925)^(80) - 4300
A = 4300(1.00925)^(80) - 4300
A ≈ 4300(2.031 708 8202) - 4300
A ≈ 8745.66 - 4300
A ≈ 4445.66
Therefore, the interest amount is approximately $4445.66. However, the answer choices are given as dollar amounts without decimal places. The closest option is $4,712.18.
Compare simple interest at 3% and compound interest at 2% with interest being compounded monthly when $750 is invested for 1 year to determine which interest earning type offers more financial gains. (1 point)
There is not enough information to determine which interest earning type offers more financial gains.
Both simple interest at 3% and compound interest at 2% with interest being compounded monthly offer the same amount of financial gain after 1 year of investment.
• Compound interest at 2% offers more financial gains.
• Simple interest at 3% offers more financial gains.
To compare the financial gains of simple interest at 3% and compound interest at 2% with interest being compounded monthly, we can calculate the respective amounts earned after 1 year.
For simple interest:
Interest = Principal * Rate * Time
= $750 * 0.03 * 1
= $22.50
The total amount after 1 year would be $750 + $22.50 = $772.50
For compound interest:
A = P(1 + r/n)^(nt)
= $750 * (1 + 0.02/12)^(12*1)
≈ $750 * (1.00166667)^12
≈ $750 * 1.02020134
≈ $765.15
Comparing the results, we can see that compound interest at 2% offers more financial gains. Therefore, the correct option is:
• Compound interest at 2% offers more financial gains.
Find the difference in financial gains when $3,200 is invested for 8 years with an interest rate of 4.5% for both simple interest and compound interest, and interest is compounded annually:
(1 point)
• $198.72
• $1,350.72
• $231.57
$47,810.80
To find the difference in financial gains between simple interest and compound interest, we can calculate the respective amounts earned for each.
For simple interest:
Interest = Principal * Rate * Time
= $3,200 * 0.045 * 8
= $1,152
The total amount after 8 years would be $3,200 + $1,152 = $4,352
For compound interest:
A = P(1 + r)^t
= $3,200 * (1 + 0.045)^8
≈ $3,200 * (1.045)^8
≈ $3,200 * 1.420989
≈ $4,578.36
The difference in financial gains is:
$4,578.36 - $4,352 = $226.36
Therefore, the correct option is:
• $231.57