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 |

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