If i take loan on 3/11/20 for $5k, 36 months, apr 10.25%. How did they cal that mo pay is $162.82 for 1st 35 mo & final pay 36 mo is $162.79? What formula do they use or how they get that calculation?

Question

The total finance charge is $861.43. 

Payments are due monthly. 

The daily rate is 0.028082. 

The first payment due date is 4/30/20. The payment is at the end of each month.

Answer 1

Monthly payments is calculated by converting % to decimal. Then use the equated monthly payment formula.

Formula: a/{[(1+r)^n]-1}/[r(1+r)^n]=p.

Answer 2

This is a forward start loan where the loan(5,000) accrues interest to the start date ( March 31). At the point the Loan balance (5000 plus accrued interest is fully amortized over 36 months). Depending upon how the loan interest is calculate for the first 19 or 20 days will change the payment amount by a penny or two.

Depending upon your day count and accrual method The balance on March 31 will be

Loan Balance 3/31 Payment

19 days 20 days 19 days 20 days

Compounding 5026.75 5028.16 162.79 162.84

Simple 5026.67 5028.08 162.79 162.83

We the use the relationship PMt/Principal =K(i,T) = (i((1+i)^T/((1+i)^T-1) or in English (sort of) i times (the FV of a dollar divided by difference of the Here, I = 10.25%/12 and T= 36 months so K = (10.25%/12)*(1+(10.25%/12))³⁶/((1+(10.25%/12)³⁶-1) = =0.023385

Hope this helps