Answer: The total value of the loan with quarterly compounded interest is $60,109.34.
Explanation:
To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = final amount (loan + interest)
P = principal (the original amount of the loan)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = time in years
For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.
Substituting the values into the formula, we get:
A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)
A = $50,000 * (1.015375)^(15.7532)
A = $50,000 * 1.22186888
A = $60,109.34
Therefore, To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = final amount (loan + interest)
P = principal (the original amount of the loan)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = time in years
For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.
Substituting the values into the formula, we get:
A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)
A = $50,000 * (1.015375)^(15.7532)
A = $50,000 * 1.22186888
A = $60,109.34
Therefore, the total value of the loan with the quarterly compounded interest would be $60,109.34.