(a) Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = amount owed after one year
P = principal (initial amount borrowed) = $7500
r = annual interest rate = 9.3% = 0.093
n = number of times interest is compounded per year = 12 (monthly)
t = time in years = 1
A = 7500(1 + 0.093/12)^(12*1) = $8227.51
Therefore, the amount owed after one year is $8227.51
(b) Using the formula for effective annual interest rate:
EAR = (1 + r/n)^n - 1
where:
EAR = effective annual interest rate
r = annual interest rate = 9.3% = 0.093
n = number of times interest is compounded per year = 12 (monthly)
EAR = (1 + 0.093/12)^12 - 1 = 0.0973 or 9.73%
Therefore, the effective annual interest rate is 9.73%.
Aldo took out a loan for $7500 that charges an annual interest rate of 9.3%, compounded monthly. Answer each part. If necessary, refer to the
list of financial formulas.
(a) Find the amount owed after one year, assuming no payments are made.
Do not round any intermediate computations, and round your answer to the nearest cent.
$
(b) Find the effective annual interest rate, expressed as a percentage.
Do not round any intermediate computations, and round your answer to the nearest hundredth of a percent.
5 answers
amount owed is actually 8,228.01
Thank you for letting me know. If the actual amount owed after one year is $8228.01, then we can adjust the answer to (a) accordingly:
(a) Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = amount owed after one year
P = principal (initial amount borrowed) = $7500
r = annual interest rate = 9.3% = 0.093
n = number of times interest is compounded per year = 12 (monthly)
t = time in years = 1
A = 7500(1 + 0.093/12)^(12*1) = $8228.01 (rounded to the nearest cent)
Therefore, the amount owed after one year is $8228.01.
(a) Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = amount owed after one year
P = principal (initial amount borrowed) = $7500
r = annual interest rate = 9.3% = 0.093
n = number of times interest is compounded per year = 12 (monthly)
t = time in years = 1
A = 7500(1 + 0.093/12)^(12*1) = $8228.01 (rounded to the nearest cent)
Therefore, the amount owed after one year is $8228.01.
Then what is the effective annual interest rate?
To find the effective annual interest rate (EAR) when the loan is compounded monthly with periodic interest rate r, we can use the formula:
EAR = (1 + r/n)^n - 1
where r is the annual interest rate, and n is the number of times the interest is compounded in a year.
In this case, r = 9.3%, and n = 12 (monthly compounding). Substituting these values into the formula, we get:
EAR = (1 + 0.093/12)^12 - 1 = 0.0973 or 9.73% (rounded to two decimal places)
Therefore, the effective annual interest rate charged on the loan is 9.73%.
EAR = (1 + r/n)^n - 1
where r is the annual interest rate, and n is the number of times the interest is compounded in a year.
In this case, r = 9.3%, and n = 12 (monthly compounding). Substituting these values into the formula, we get:
EAR = (1 + 0.093/12)^12 - 1 = 0.0973 or 9.73% (rounded to two decimal places)
Therefore, the effective annual interest rate charged on the loan is 9.73%.