What is the monthly payment for a loan of $149 383.00 with an interest rate of 5.15% per annum, compounded semi-annually? The term of the loan is 5.5 years
To calculate the monthly payment for this loan, we first need to determine the number of compounding periods within the loan term. Since the interest is compounded semi-annually (twice a year) and the loan term is 5.5 years, there will be a total of 11 compounding periods.
Next, we calculate the periodic interest rate:
Periodic interest rate = annual interest rate / compounding periods per year
Periodic interest rate = 5.15% / 2 per year
Periodic interest rate = 2.575% per compounding period
Now we can use the formula for calculating the monthly payment on a loan:
Monthly payment = Pmt * [r(1+r)^n] / [(1+r)^n - 1]
where:
Pmt = loan amount = $149 383.00
r = periodic interest rate = 2.575% or 0.02575
n = number of payments = 11
Plugging in the values, we get:
Monthly payment = $149 383.00 * [0.02575(1+0.02575)^11] / [(1+0.02575)^11 - 1]
Monthly payment = $149 383.00 * [0.02575(1.29477)] / [1.29477 - 1]
Monthly payment = $149 383.00 * [0.03335] / [0.29477]
Monthly payment = $149 383.00 * 0.1131
Monthly payment ≈ $16 907.45
Therefore, the monthly payment for a loan of $149 383.00 at an interest rate of 5.15% per annum, compounded semi-annually, with a term of 5.5 years is approximately $16 907.45.