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Michelle borrows $100 000. The interest rate charged is 12% per annum compounded monthly. The monthly payment is $1029 and the first repayment is made after one month.
What is the amount outstanding immediately after the SECOND monthly repayment is made? (3 marks)
--- 6 WORK AREA LINES (style=lined) ---
`$99\ 941.71`
| `text(Interest per month)` | `= text(12%)/12= 1text(%)` |
`text(Let)\ \ A=\ text(amount owing)`
`text(After 1st repayment:)`
| `A_1` | `= (100\ 000 + text(1%) xx 100\ 000) – 1029` |
| `= $99\ 971` |
`text(After 2nd repayment:)`
| `A_2` | `= (99\ 971 + text(1%) xx 99\ 971) – 1029` |
| `= $99\ 941.71` |
Bill borrows $420 000 to buy a house. Interest is charged at 7.2% per annum, compounded monthly.
How much does he owe at the end of the first month, after he has made a $4000 repayment?
`B`
`text(Let)\ \ L\ =\ text(Amount of the loan after 1 month)`
`r= (7.2 text(%))/12=0.6 text(%)\ =0.006`
`text(Using)\ \ FV=PV(1+r)^n`
| `L` | `= 420\ 000 (1 + 0.006)^1 – text(repayment)` |
| `= 420\ 000 (1.006) – 4000` | |
| `= $418\ 520` |
`=> B`