Question

Financial Math: A 20-year loan is being repaid by annual payments of 2000, 2500, 3000, 3500, ... at end of each year. If the present value of the seventh and eighth payments are equal. (a) Find the annual effective interest rate. (b) Find the principal and interest paid in the third annual payment.

Please show algebraic work not just excel.

Answer 1

1.
7th payment=2000+500*(7-1)=5000
8th payment=2000+500*(8-1)=5500
5000=5500/(1+r)
=>r=10%

2.
Loan amount=2000/1.1+2500/1.1^2+3000/1.1^3+3500/1.1^4+4000/1.1^5+4500/1.1^6+5000/1.1^7+5500/1.1^8+6000/1.1^9+6500/1.1^10+7000/1.1^11+7500/1.1^12+8000/1.1^13+8500/1.1^14+9000/1.1^15+9500/1.1^16+10000/1.1^17+10500/1.1^18+11000/1.1^19+11500/1.1^20=44730.58324

Beginning amount	Interest	Principal	Total payment	Ending balance
44730.58324	4473.058324	-2473.058324	2000	47203.64156
47203.64156	4720.364156	-2220.364156	2500	49424.00572
49424.00572	4942.400572	-1942.400572	3000	51366.40629