Here are some step-by-step calculations so you can see fairly clearly what's going on:-

The effective annual interest rate is given by

ear = (1 + i/n)^n - 1

where i is the nominal interest rate and n is the number of compounding periods.

ear = (1 + 0.1/12)^12 - 1 = 0.104713 = 10.4713 %

The monthly rate is

r = (ear + 1)^(1/n) - 1 = 0.00833333 = 0.833333 %

The monthly repayment is given by the formula

p = r*pv/(1 - (1 + r)^-n)

where pv is the present value of the loan

p = 0.00833333*1000/(1 - (1 + 0.00833333)^-12) = 87.9159

This gives a total repayment of p*12 = 1054.99

You might have expected the loan to cost (1 + ear)*pv = (1 + 0.104713)*1000 = 1104.71 but the repayments progressively reduce the amount owed so the total repayment is only 1054.99.

Here are some step-by-step calculations so you can see fairly clearly what's going on:-

The effective annual interest rate is given by

ear = (1 + i/n)^n - 1

where i is the nominal interest rate and n is the number of compounding periods.

ear = (1 + 0.1/12)^12 - 1 = 0.104713 = 10.4713 %

The monthly rate is

r = (ear + 1)^(1/n) - 1 = 0.00833333 = 0.833333 %

The monthly repayment is given by the formula

p = r*pv/(1 - (1 + r)^-n)

where pv is the present value of the loan

p = 0.00833333*1000/(1 - (1 + 0.00833333)^-12) = 87.9159

This gives a total repayment of p*12 = 1054.99

You expected the loan to cost (1 + ear)*pv = (1 + 0.104713)*1000 = 1104.71 but the repayments progressively reduce the amount owed so the total repayment is only 1054.99.

The effective annual interest rate is given by

ear = (1 + i/n)^n - 1

where i is the nominal interest rate and n is the number of compounding periods.

ear = (1 + 0.1/12)^12 - 1 = 0.104713 = 10.4713 %

The monthly rate is

r = (ear + 1)^(1/n) - 1 = 0.00833333 = 0.833333 %

The monthly repayment is given by

p = r*pv/(1 - (1 + r)^-n)

where pv is the present value of the loan

p = 0.00833333*1000/(1 - (1 + 0.00833333)^-12) = 87.9159

This gives a total repayment of p*12 = 1054.99

Here are some step-by-step calculations so you can see fairly clearly what's going on:-

The effective annual interest rate is given by

ear = (1 + i/n)^n - 1

where i is the nominal interest rate and n is the number of compounding periods.

ear = (1 + 0.1/12)^12 - 1 = 0.104713 = 10.4713 %

The monthly rate is

r = (ear + 1)^(1/n) - 1 = 0.00833333 = 0.833333 %

The monthly repayment is given by the formula

p = r*pv/(1 - (1 + r)^-n)

where pv is the present value of the loan

p = 0.00833333*1000/(1 - (1 + 0.00833333)^-12) = 87.9159

This gives a total repayment of p*12 = 1054.99

You might have expected the loan to cost (1 + ear)*pv = (1 + 0.104713)*1000 = 1104.71 but the repayments progressively reduce the amount owed so the total repayment is only 1054.99.