Loan repayments calculation in C++ - c++

Question

I'm writing a program which will calculate monthly payments for a loan. It is not giving the correct answer though. Here is my code:
#include<iostream>
#include<cmath>
using namespace std;
int main()
{
double YearlyInt, LoanAmount, Payment, AmountPaid, MonthlyInt;
int NumPayments;
cout << "Enter the loan amount (LoanAmount) --> ";
cin >> LoanAmount;
cout << "Enter the YEARLY interest rate as a percentage --> ";
cin >> YearlyInt;
cout << "Enter number of payments --> ";
cin >> NumPayments;
cout << "Loan amount: " << LoanAmount << endl;
cout << "Yearly Interest Rate: " << YearlyInt << "%" << endl;
cout << "Number of Payments: " << NumPayments << endl;
MonthlyInt = YearlyInt / 12;
Payment = MonthlyInt * pow (( 1 + MonthlyInt ), NumPayments) / (pow(( 1 + MonthlyInt), NumPayments) -1) * LoanAmount;
cout << "Monthly Payment: " << Payment << endl;
AmountPaid = Payment * 36;
cout << "Amount Paid Back: " << AmountPaid << endl;
cout << "Interest Paid: " << (AmountPaid - LoanAmount) << endl;
cout << "Program Over" << endl << endl << endl << endl;
cout << "Press Enter to end -->" << endl;
return 0;
}
The program uses this formula:
MonthlyInt * pow(1 + MonthlyInt, NumPayments) * LoanAmount
Payment = ---------------------------------------------------------------
pow(1 + MonthlyInt, NumPayments) - 1
This is what I get as an output:
Enter the loan amount (LoanAmount) --> 10000
Enter the YEARLY interest rate as a percentage --> 12
Enter number of payments --> 36
Loan amount: 10000
Yearly Interest Rate: 12%
Number of Payments: 36
Monthly Payment: 10000
Amount Paid Back: 360000
Interest Paid: 350000
Program Over
Press Enter to end -->
Press any key to continue . . .
As you can see, the Loan amount is clearly wrong. How can I fix my code?

Answer 1

Step 1: MonthlyInt does NOT equal YearlyInt / 12 because of the effect of compounding interest. The general formula for converting between rate of a smaller period and the equivalent rate of a larger period is: (1 + r) ^n = 1 + R. So in this case r = MonthlyInt and R = YearlyInt. Therefore, the first order of business is to change
from:
MonthlyInt = YearlyInt / 12;
to:
MonthlyInt = pow ( (1.0 + YearlyInt) , (1.0/NumPayments) ) - 1.0; // note decimals!
Step 2: Add a line that prints MonthlyInt so that you can verify the calculation. :)
Step 3: Change AmountPaid = Payment * 36; to AmountPaid = Payment * NumPayments;
Step 4: Optionally, add dollar signs and clean up the decimals.
We must add the header #include<iomanip>, then set the number of decimals with cout << setprecision(n) << fixed << whateverVariable, where n equals the number of decimal places you want.
Revised code:
#include<iostream>
#include<cmath>
#include<iomanip>
using namespace std;
int main()
{
double YearlyInt = -1, LoanAmount = -1, Payment = -1, AmountPaid = -1, MonthlyInt = -1;
int NumPayments;
cout << "Enter the loan amount (LoanAmount) --> ";
cin >> LoanAmount;
cout << "Enter the YEARLY interest rate as a decimal number (e.g. 3.25% as .0325) --> ";
cin >> YearlyInt;
cout << "Enter number of payments --> ";
cin >> NumPayments;
cout << "Loan amount: $" << setprecision(2) << fixed << LoanAmount << endl;
cout << "Yearly Interest Rate: " << setprecision(3) << YearlyInt * 100 << "%" << endl;
cout << "Number of Payments: " << NumPayments << endl;
MonthlyInt = pow ( (1.0 + YearlyInt) , (1.0/NumPayments) ) - 1.0;
cout << "MonthlyInt: " << MonthlyInt*100 << "%" << endl;
Payment = MonthlyInt * pow (( 1 + MonthlyInt ), NumPayments) / (pow(( 1 + MonthlyInt), NumPayments) -1) * LoanAmount;
cout << "Monthly Payment: $" << setprecision(2) << Payment << endl;
AmountPaid = Payment * NumPayments;
cout << "Amount Paid Back: $" << AmountPaid << endl;
cout << "Interest Paid: $" << (AmountPaid - LoanAmount) << endl;
cout << "Program Over" << endl << endl << endl << endl;
cout << "Press Enter to end -->" << endl;
return 0;
}
Assumptions: the loan has a no-fees APR of YearlyInt to be compounded monthly, with monthly payments, with the first payment applied on the last day of the same month in which the loan is originated, and with all “on time” payments (whatever that is defined as, by the lendor) being applied as if paid on the last day of the applicable period.

Answer 2

There are a few problems:
You enter rate in percents, so convert them to a decimal number: MonthlyInt/100.0
Your number of payments should be either fixed, or entered by user. Now it is firstly read in, but then there is 36 used in the code. It should be replaced with the proper variable.
Be careful with integer division. There is no mistake at the moment, but to avoid such, use 1.0 and 100.0 instead of just 1 and 100 if you want to be sure you have floats.
Be sure your math is right. In fact, this should be the very first thing you do. This is a programming site though, so it's off-topic here.
(optional) Conventionally, variable names shouldn't start with capital letter.

Answer 3

Here is a program which correctly calculates the payments assuming the following:
Yearly interest is calculated as compounded monthly interest.
There are no fees applied to the loan.
The repayments start one month after the loan is given.
The monthly payment amounts do not change.
No monthly payments are missed.
.
#include<iostream>
#include<cmath>
using namespace std;
int main()
{
double YearlyInt, LoanAmount, Payment, AmountPaid, MonthlyInt;
int NumPayments;
cout << "Enter the loan amount (LoanAmount) --> ";
cin >> LoanAmount;
cout << "Enter the YEARLY interest rate as a percentage --> ";
cin >> YearlyInt;
cout << "Enter number of monthly payments --> ";
cin >> NumPayments;
cout << "Loan amount: " << LoanAmount << endl;
cout << "Yearly Interest Rate: " << YearlyInt << "%" << endl;
cout << "Number of Monthly Payments: " << NumPayments << endl;
MonthlyInt = pow( 1 + YearlyInt/100, 1.0/12 );
Payment = LoanAmount * pow( MonthlyInt, NumPayments ) *
( MonthlyInt - 1 ) /
( pow( MonthlyInt, NumPayments ) - 1 );
cout << "Monthly Payment: " << Payment << endl;
AmountPaid = Payment * NumPayments;
cout << "Amount Paid Back: " << AmountPaid << endl;
cout << "Interest Paid: " << (AmountPaid - LoanAmount) << endl;
cout << "Program Over" << endl << endl << endl << endl;
return 0;
}

Answer 4

Is the program supposed to calculate compound interest or simple interest?
Your calculation appears to be incorrect. You calculate a monthly interest rate, which makes it look like simple interest, but you use pow, which indicates something to do with compound interest. You should probably look into that.

Answer 5

#include<iostream>
#include<cmath>
using namespace std;
int main()
{
double YearlyInt, LoanAmount, Payment, AmountPaid, MonthlyInt, NumPayments;
cout << "Enter the loan amount (LoanAmount) --> ";
cin >> LoanAmount;
cout << "Enter the YEARLY interest rate as a percentage --> ";
cin >> YearlyInt;
cout << "Enter number of payments --> ";
cin >> NumPayments;
cout << "Loan amount: " << LoanAmount << endl;
cout << "Yearly Interest Rate: " << YearlyInt << "%" << endl;
cout << "Number of Payments: " << NumPayments << endl;
MonthlyInt = (YearlyInt/100.0) / 12;
Payment = MonthlyInt * pow (( 1 + MonthlyInt ), NumPayments) / (pow(( 1 + MonthlyInt), NumPayments) -1) * LoanAmount;
cout << "Monthly Payment: " << Payment << endl;
AmountPaid = Payment * 36;
cout << "Amount Paid Back: " << AmountPaid << endl;
cout << "Interest Paid: " << (AmountPaid - LoanAmount) << endl;
cout << "Program Over" << endl << endl << endl << endl;
cout << "Press Enter to end -->" << endl;
return 0;
Got it simply switched MonthlyInt = YearlyInt / 12; to MonthlyInt = (YearlyInt/100.0) / 12;

Answer 6

#include<iostream>
#include<cmath>
using namespace std;
int main()
{
double YearlyInt, LoanAmount, Payment, AmountPaid, MonthlyInt, NumPayments;
cout << "Enter the loan amount (LoanAmount) --> ";
cin >> LoanAmount;
cout << "Enter the YEARLY interest rate as a percentage --> ";
cin >> YearlyInt;
cout << "Enter number of payments --> ";
cin >> NumPayments;
cout << "Loan amount: " << LoanAmount << endl;
cout << "Yearly Interest Rate: " << YearlyInt << "%" << endl;
cout << "Number of Payments: " << NumPayments << endl;
MonthlyInt = (YearlyInt/100.0) / 12;
Payment = MonthlyInt * pow (( 1 + MonthlyInt ), NumPayments) / (pow(( 1 + MonthlyInt), NumPayments) -1) * LoanAmount;
cout << "Monthly Payment: " << Payment << endl;
//correction to Amount paid Value
AmountPaid = Payment * NumPayments;
cout << "Amount Paid Back: " << AmountPaid << endl;
cout << "Interest Paid: " << (AmountPaid - LoanAmount) << endl;
cout << "Program Over" << endl << endl << endl << endl;
cout << "Press Enter to end -->" << endl;
return 0;
}

Answer 7

In case you don't want to use pow functions, you can directly calculate the geometric sum and nth term of the series yourself (the pow() comes from geometric terms and sum). See the proof here: https://mortgagecalculator.mes.fm/amortization-formula-proof
int months = 60;
float principle = 10000;
float rate = 6.5f/100;
float monthly_factor = 1 + rate / 12;
float temp = 1, temp2= monthly_factor;
for(int i = 0;i < months - 1; i++){ //this for loop calculates the geometric sum with ratio of monthly_factor in temp and pow(monthly_factor,n) in temp2
temp *= monthly_factor;
temp2 *= monthly_factor;
temp += 1;
}
float monthly_payment = principle * temp2 / temp;