A bank loan of $500 is arranged to be repaid in two years by equal monthly instalments. Interest, calculated monthly, is charged at 11% p.a on the remaining debt. Calculate the monthly repayment if the first repayment is to be made one month after the loan is granted.
let the payment be p
then i = .11/12 = .009166..
500 = p(1 - 1.0091666..^-24)/.0091666..
You do the button-pushing
To calculate the monthly repayment, we need to find the equal monthly instalments for a loan of $500 over two years, with interest calculated monthly at a rate of 11% per annum.
Step 1: Convert the annual interest rate to a monthly rate.
Since the interest is calculated monthly, we need to convert the annual interest rate of 11% to a monthly rate.
Monthly interest rate = Annual interest rate / 12
= 11% / 12
= 0.9166% (approx.)
Step 2: Calculate the number of months in two years.
As the loan is to be repaid over two years, we need to calculate the total number of months.
Number of months = 2 years * 12 months/year
= 24 months
Step 3: Calculate the monthly repayment using the formula for the equal monthly instalment:
Monthly repayment = Loan amount / Present value interest factor of an annuity
The present value interest factor of an annuity can be calculated using the following formula:
Present value interest factor of an annuity = [1 - (1 + r)^(-n)] / r
Where:
r = Monthly interest rate (in decimal form)
n = Number of months
Substituting the given values into the formula:
Monthly interest rate = 0.9166% / 100 = 0.009166 (as a decimal)
Present value interest factor of an annuity = [1 - (1 + 0.009166)^(-24)] / 0.009166
Calculating this value:
Present value interest factor of an annuity ≈ 17.1928
Now, we can calculate the monthly repayment:
Monthly repayment = Loan amount / Present value interest factor of an annuity
= $500 / 17.1928
Calculating this value:
Monthly repayment ≈ $29.06 (rounded to the nearest cent)
Therefore, the monthly repayment, if the first repayment is to be made one month after the loan is granted, is approximately $29.06.
To calculate the monthly repayment for a bank loan with equal monthly installments and monthly interest, we can use the formula for the monthly repayment amount of an amortizing loan.
The formula for the monthly repayment amount is:
R = P * (r * (1 + r)^n) / ((1 + r)^n - 1),
where:
R is the monthly repayment amount,
P is the principal loan amount,
r is the monthly interest rate, and
n is the number of monthly repayments.
Let's break down the given information to find the values needed for the formula.
Principal loan amount (P): $500
Monthly interest rate (r): The annual interest rate is given as 11%, so we need to convert it into a monthly interest rate. Divide the annual interest rate by 12 to get the monthly interest rate: 11% / 12 = 0.92%.
Number of monthly repayments (n): The loan is to be repaid in two years, so there will be 12 monthly repayments in total.
Now, we can plug in the values into the formula:
R = $500 * (0.92% * (1 + 0.92%)^12) / ((1 + 0.92%)^12 - 1).
Using a calculator or a spreadsheet, calculate the value of R.
R ≈ $46.95.
Therefore, the monthly repayment amount for this loan is approximately $46.95.