Question

Using the equal-payment series formula, calculate the monthly payment for a project whose loan is $10,000,000 paid over 360 months at an effective annual interest rate of 6.17%.

Note: Interest rate is yearly so n, time and i, interest rate must match.

Also note: effective vs. nominal interest rate.

Answer 1

Loan Amount P = $10000000

Interest Rate = 6.17% or 0.0617/12 monthly

Number of payment periods = n = 360 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 10000000*( 0.0617/12)*(1+ 0.0617/12)³⁶⁰/((1+ 0.0617/12)³⁶⁰-1) = $61,052.36