Question

Both Hannah and Richard took out $15,000 loans to assist in paying for their post-secondary tuition. Hannah was offered a rate of 4.35% compounded semi-annually, while Richard was offered a rate of 3.5% compounded monthly. Both have agreed to repay the debt in a single payment, 4 years from the date of borrowing. Who will have to pay more to clear their debt, and by how much, as a result of their differing interest rates?

Answer 1

Interest = Beginning Outstanding amount * Interest * Period of interest/Number of months in an year

Ending outstanding amount = Beginning Outstanding amount + Interest

0.5 resembles 6 months, 0.25 resembles 3 months in an year.

HANNAH
Year	Beginning outstanding Amount	Interest	Ending outstanding Amount
0.5	15000	326.25	15326.25
1	15326.25	333.3459	15659.59594
1.5	15659.59594	340.5962	16000.19215
2	16000.19215	348.0042	16348.19633
2.5	16348.19633	355.5733	16703.7696
3	16703.7696	363.307	17067.07659
3.5	17067.07659	371.2089	17438.2855
4	17438.2855	379.2827	17817.56821

RICHARD
Year	Beginning outstanding Amount	Interest	Ending outstanding Amount
0.25	15000	131.25	15131.25
0.5	15131.25	132.3984	15263.64844
0.75	15263.64844	133.5569	15397.20536
1	15397.20536	134.7255	15531.93091
1.25	15531.93091	135.9044	15667.8353
1.5	15667.8353	137.0936	15804.92886
1.75	15804.92886	138.2931	15943.22199
2	15943.22199	139.5032	16082.72518
2.25	16082.72518	140.7238	16223.44903
2.5	16223.44903	141.9552	16365.40421
2.75	16365.40421	143.1973	16508.60149
3	16508.60149	144.4503	16653.05176
3.25	16653.05176	145.7142	16798.76596
3.5	16798.76596	146.9892	16945.75516
3.75	16945.75516	148.2754	17094.03052
4	17094.03052	149.5728	17243.60329

Hannah ahs to pay more than richard by 573.9649$(17817.56821 - 17243.60329), beacuse of their interest rates.