Question

Three years ago Jane borrowed 7500 from Mary. The condition was that she would pay her back in seven years time at an interest rate of 11.21% per year, compounded semi-annually. Six months ago she also borrowed 25000 from Mary at 9.45% per year, compounded monthly. Jane would like to pay off her debt four years from now. The amount of money that Jane will have to pay Mary four years from now equals

1) 36607.98

2) 45181.81

3) 48032.20

4) 54278.92

5) 55336.49

Answer 1

11.21% per annum is 5.605% semiannually. Jane borrowed the money 3 years ago and is due to repay in 7 years' time, which makes the total loan time 10 years, or 20 periods of 6 months. So the total amount she would have to pay in 7 years' time is  7500*1.05605^20=22322.91. To pay this off in 4 years' time, we reduce the time to pay by 3 years or 6 half-years. So the amount would instead be 7500*1.05605^14=16093.26.

9.45% annually is 9.45/12=0.7875% per month. The period is 6+48=54 months, so the amount in 4 years' time is 25000*1.007875^54=38185.66. If she combines both debts she will be paying 38185.66+16093.26=54278.92 (answer 4).