Question

How much interest will be paid in the 7^th month if you borrow $20,000 at a rate of 6%, compounded monthly, and pay it off over 6 years?

1. $89.04
2. $92.97
3. $237.30
4. $329.81

Answer 1

Monthly Loan Payment

Loan Amount (P) = $20,000

Monthly Interest Rate (n) = 0.50% per month [6% / 12 Months]

Number of months (n) = 72 Months [6 Years x 12 months]

Monthly Loan Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$20,000 x {0.05 x (1 + 0.05)⁷²}] / [(1 + 0.05)⁷² – 1]

= [$20,000 x {0.05 x 1.432044}] / [1.432044 – 1]

= [$20,000 x 0.007160] / 0.432044

= $143.20 / 0.432044

= $331.46 per month

Loan amortization schedule for the first seven months

Month	Beginning Balance	Total Payment	Interest Paid at 0.50%	Principal Paid	Ending Balance
1	20,000.00	331.46	100.00	231.46	19,768.54
2	19,768.54	331.46	98.84	232.62	19,535.92
3	19,535.92	331.46	97.68	233.78	19,302.14
4	19,302.14	331.46	96.51	234.95	19,067.19
5	19,067.19	331.46	95.34	236.12	18,831.07
6	18,831.07	331.46	94.16	237.30	18,593.76
7	18,593.76	331.46	92.97	238.49	18,355.27

“Hence, the interest will be paid in the 7th month = $92.97”