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$15 000 is invested for 12 months.
For the first six months the interest rate is 6.1% per annum compounding monthly.
After six months the interest rate increases to 6.25% per annum compounding monthly.
Calculate the total interest earned by this investment over 12 months, giving your answer to the nearest dollar. (4 marks)
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`$953`
`text{In the first 6 months:}`
`text{Interest rate}\ (r) = \frac{0.061}{12}`
| `FV(\text{after 6 months})` | `=PV(1+r)^n` | |
| `=15\ 000(1 + \frac{0.061}{12})^6` | ||
| `=$15\ 463.35…` |
`text{In the second 6 months:}`
`text{Interest rate}\ (r) = \frac{0.0625}{12}`
| `FV(\text{after 2nd 6 months})` | `=15\ 463.35(1 + \frac{0.0625}{12})^6` | |
| `=$15\ 952.91…` |
| `:.\ text(Interest)` | `= 15\ 952.91-15\ 000` |
| `= $953\ \ \text{(nearest dollar)}` |