A 10-year loan of 120,000 is to be repaid with payments at the end of each...

A 10-year loan of 120,000 is to be repaid with payments at the end of each month. Interest is at an annual effective rate of 6.00%.

The first monthly payment is 800. Each additional payment will be k more than the previous month payment. Find k.

Expert Solution

rate compounded monthly=((1+6%)^(1/12)-1)*12=5.8411%

The given annuity can be broken into two streams
Stream 1: Constant annuity of 800
Present Value=800/(5.8411%/12)*(1-1/(1+5.8411%/12)^(12*10))=72579.32783

Stream 2: Arithmetic gradient annuity of k

Present Value=k/(5.8411%/12*(1+5.8411%/12)^(12*10))*(((1+5.8411%/12)^(12*10)-1)/(5.8411%/12)-12*10)=4872.44843*k

Total Value=72579.32783+4872.44843*k

=>72579.32783+4872.44843*k=120000

=>k=(120000-72579.32783)/4872.44843

=>k=9.732411302

jeff jeffy answered 1 year ago

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