It is now the end of May 2015. Peter is planning to leave the country at the end of the year.

Question

He has 3 debtors each owing him an amount of 15 000. Sam must pay his 15 000 back in three months time from now, Jane hers in five months time from now, and Ben his in seven months time from now. Peter tells them that it will be all right if they each pay him back just before he leaves at the end of December 2015. However, he will charge simple interest rate at 10% from the time that they were each supposed to pay back the amount of 15 000. The amount that Peter will receive at the end of December 2015 will equal:

1. 45 750

2. 45 757.33

3. 46 875

4. 47 625

5. None of the above

Answer 1

To work this out we have to sort out the calendar. Now is the end of May 2015, and at the end of December, 7 months away, Peter is leaving. He's owed 45000 by three people and wants that money before he leaves. Ben has until the end of December to pay his share, so he will not have any interest to pay on his 15000. Jane has to pay her share by the end of October or she will have 10% interest to pay for November and December. 10% is the rate over a year so, since two months is a sixth of a year, she will pay 10/6=5/3=1.67% on her 15000=5/3*15000/100=250. Sam's payment is due at the end of August, so he will have 4 months' interest to pay and his rate will be 10/3% for one third of a year and his interest will be 10/3*15000/100=500 (twice as much as Jane because he's paying interest twice as long as Jane is). So on top of the 45000 owed to Peter, he will have gained 500+250=750 interest, making the total amount 45750 (answer 1).