How can I calculate maximum Loan amount?

Question

I want to calculate max loan amount a client can get having this info:

1. loan terms in years
2. Interest Rate Percentage
3. Max Monthly payment
4. The loan Interest calculation is semi annual compounding

I have used this formula:

termInMonths = termInyears * 12;
monthlyInterestRate = InterestRatePercentage / 1200;
maxLoanAmount = maxMonthlyPayment * ((((1 + monthlyInterestRate) ^ termInMonths) - 1) / (monthlyInterestRate * ((1 + monthlyInterestRate) ^ termInMonths)));

I have also tried this formula (http://www.financeformulas.net/Present_Value_of_Annuity.html):

termInMonths = termInyears * 12;
monthlyInterestRate = InterestRatePercentage / 1200;
maxLoanAmount = maxMonthlyPayment * ((1 - ((1 + monthlyInterestRate) ^ (-termInMonths))) / monthlyInterestRate)

But the results does not match. I am trying to mach the results with Canadian Mortgage and Housing Corporation https://www.cmhc-schl.gc.ca/en/co/buho/buho_020.cfm

Any help is appreciated.

Answer 1

The interest rate should be calculated as follow (compounding is 2 for semi annual):

compounding = 2; monthlyInterestRate = ((1 + (InterestRatePercentage / compounding)) ^ (compounding / 12)) - 1;

Answer 2

Amount borrowed = Principal = P (in dollar)..

Interest Rate = R% p.a.

Total number of Installments = N. [If the loan is borrowed for n years and the compounding period is semi-annually, then N = 2n.]

Fixed Repayment per Installment = S (in dollar)

To make all later calculations easier, we let X = 1 + R/200 [because the compounding period is semi-annually.].

Try $S = PX^N \dfrac {(X – 1 )}{(X^N – 1)}$

Just re-arrange the above to make P as the subject.