Brenda takes out a twenty year loan of R400,000..she repays the loan by means of equal montly payments starting one month after the granting of the loan.the interest rate is 16% per annum compounded montly. calculate the montly instalments.
R4976 per month.
To calculate the monthly installments, we can use the formula for the monthly payment on a loan, also known as the Amortization Formula. The formula is given as:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal amount (loan amount)
r = monthly interest rate
n = number of payments (in this case, the total number of months)
First, let's convert the annual interest rate of 16% to a monthly interest rate. The monthly interest rate is calculated by dividing the annual interest rate by 12.
r = 16% / 12 = 0.16 / 12 = 0.0133 (rounded to four decimal places)
Next, calculate the total number of payments (n) for a twenty-year loan. Since there are 12 months in a year, the total number of payments will be:
n = 20 years * 12 months/year = 240 months
Now we have all the values needed to plug into the Amortization Formula:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
M = (400,000 * 0.0133 * (1 + 0.0133)^240) / ((1 + 0.0133)^240 - 1)
Using a calculator, simplify the equation to find the monthly installment (M). The monthly installment will be the result of this calculation.