Question

You borrowed $800 at 6% compounded annually. Approximately how many years will you make payments on the loan if:

A. your annual payment is $60?

B. your annual payment is $48? (Hint: Why did the calculator provide an answer if the payment is $60, while returning an “error” message if the payment is $48? What would the answer be if the payment were $51? $55? $59?).

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Answer 1

A.

Closing Princi pal (opening-princ ipal repaymen t) Opening Princi pal |(previous closi ng) Principal Repa Interest yment (opening*0.0 6) Year Installment |(installment-in terest) 48 788 800 60 12 47.28 775.28 788 60 12.72 3 775.28 46.5168 60 13.4832 761.7968 45.707808 747.504608 4 761.7968 60 14.292192 747.504608 5 44.85027648 60 15.14972352 732.3548845 732.3548845 43.94129307 60 16.05870693 716.2961775 716.2961775 42.97777065 60 17.02222935 699.2739482 681.2303851 8 699.2739482 41.95643689 60 18.04356311 681.2303851 40.87382311 9. 60 19.12617689 662.1042082 10 662.1042082 39.72625249 60 20.27374751 641.8304607 11 641.8304607 38.50982764 60 21.49017236 620.3402883 12 620.3402883 37.2204173 60 22.7795827 597.5607056 13 597.5607056 35.85364234 60 24.14635766 573.414348 14 573.414348 34.40486088 60 25.59513912 547.8192088 15 547.8192088 32.86915253 60 27.13084747 520.6883614 520.6883614 31.24130168 28.75869832 491.9296631 30.48422022 461.4454428 32.31327343 429.1321694 16 60 17 491.9296631 29.51577978 60 18 461.4454428 27.68672657 60 429.1321694 25.74793017 19 60 34.25206983 394.8800996 20 394.8800996 23.69280597 60 36.30719403 358.5729056 358.5729056 21.51437433 320.0872799 19.20523679 21 60 38.48562567 320.0872799 22 60 40.79476321 279.2925167 23 279.2925167 16.757551 60 43.242449 236.0500677 236.0500677 14.16300406 45.83699594 190.2130717 24 60 25 190.2130717 11.4127843 60 48.5872157 141.6258561 26 141.6258561 8.497551363 60 51.50244864 90.12340741 27 90.12340741 5.407404445 60 54.59259556 35.53081186 28 35.53081186 2.131848712 37.66266057 35.53081186

Therefore, 28 years.

B.

Refer to the interest of 1st year in the table above.

Interest is 6% and principal is 800. Therefore, interest will be $48.

If we pay only $48, it will only repay the interest of the year and principal repayment will be zero, resulting into opening principal of 800 in 2nd year also. This can go upto infinity, because every year interest will be $48 and we will keep on paying that and principal will always be 800 outstanding and it will NEVER get repaid, till perpetuity.

In case of any installment above $48, some portion of the principal will be repaid. Therefore, the principal will become 0 one day.

So, from this we can concude that Installment amount should be MORE THAN the interest for the 1st period, otherwise, principal will never be paid at all and loan will never end. And, it will result in an error.

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