Question

# Financial Math: A 20-year loan is being repaid by annual payments of 2000, 2500, 3000, 3500,...

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.

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