Answer to Question #277518 in Financial Math for Dae

Question

A loan of 10000 is to be repaid over 10 years by a level annuity payable monthly in arrears. The amount of the monthly payment is calculated on a basis od an interest rate of 1% per month effective,. For which monthly repayment the capital first exceeds the interest

Answer 1

$10000=R\frac{1-1.01^{-10\cdot12}}{0.01}$

monthly repayment:

$R=143.47$

$FV=\frac{R((1+i)^n-1)}{i}=10000$

monthly repayment when the capital first exceeds the interest:

$n=ln(\frac{10000i}{R}+1)/ln(1+i)=53.15$ months

Answer: 54-th month