Question

1. You take out a $20,000, ten-year loan. Equal payments are to be made at the end of each year at an interest rate of 10%. Calculate the appropriate loan table, showing the breakdown in each year between principal and interest.

Cost	20,000
Payment	$3,254.91
Interest	10%
Years	10
			Division of payment between:
Year	Principal at beginning of year	Payment at end of year	Interest	Principal
1
2
3
4
5
6
7
8
9
10
	0.00

Answer 1

Annual end-of-year loan payment

Loan Amount (P) = $20,000

Annual Interest Rate (n) = 10% per year

Number of years (n) = 10 Years

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

= [$20,000 x {0.10 x (1 + 0.10)¹⁰}] / [(1 + 0.10)¹⁰ – 1]

= [$20,000 x {0.10 x 2.59374}] / [2.59374 – 1]

= [$20,000 x 0.25937] / 1.59374

= $5,187.48 / 1.59374

= $3,254.91 per year

“The Annual end-of-year loan payment = $3,254.91 per year”

Loan Amortization Schedule

Year	Principal at beginning of year ($)	Payment at end of year ($)	Interest Paid at 10% ($)	Principal ($)
1	20,000.00	3,254.91	2,000.00	1,254.91
2	18,745.09	3,254.91	1,874.51	1,380.40
3	17,364.69	3,254.91	1,736.47	1,518.44
4	15,846.25	3,254.91	1,584.62	1,670.29
5	14,175.96	3,254.91	1,417.60	1,837.31
6	12,338.65	3,254.91	1,233.86	2,021.05
7	10,317.60	3,254.91	1,031.76	2,223.15
8	8,094.45	3,254.91	809.45	2,445.46
9	5,648.99	3,254.91	564.90	2,690.01
10	2,958.98	3,254.91	295.93	2,958.98