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Sequences & Series - Geometric - Loans.
Test Yourself 1.


 

 
  2. David is saving to buy a new car. He is planning to spend $16,000 on the car.

He already has $7,500 saved and he did consider putting an increasing amount of money aside from his wages on a monthly basis.

As that proposition was not going to be satisfactory, he is now considering taking out a car loan. The bank suggested he retain $2,500 from his savings to cover other purchase expenses and so offered a loan on a weekly repayment option on the $11,000 balance of his savings for 4 years at 8% reducible interest.

(i) How much would the repayments cost David each week?

(ii) Comment of that amount compared to his first plan.
 

 
   
 

 
   
Additional repayment during the term.

Rory borrows $100,000 to be repaid at a reducible interest rate of 7.2% p.a..

Let $An be the amount still owing at the end of n months and $M be the monthly repayments.

(i) Show that A2 = 100,000 (1.006)2 - M(1 + 1.006 + 1.0062).

(ii) Show that .

(iii) Rory makes monthly repayments of $780. How many years and months will it take to repay the loan?

(iv) Show that after making 120 monthly repayments, the amount owing is $68,500 to the nearest $100.

(v) Immediately after making the 120th payment, Rory makes a one-off payment of $20,000. The interest rate and the monthly repayment remain the same.

After how many more months will the amount owing be completely repaid?