Aussie Maths & Science Teachers: Save your time with SmarterEd
It is estimated that inflation will average 3.5% per annum over the next eight years.
If a new machine costs $60 000 now, calculate the cost of a similar new machine in eight years time, adjusted for inflation. Assume no other cost change.
Write your answer correct to the nearest dollar. (2 marks)
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`$79\ 008.54`
| `FV` | `= PV(1+r)^n` |
| `= 60\ 000(1.035)^8` | |
| `= $79\ 008.54\ \ \text{(nearest cent)}` |
In Japan, a bowl of ramen cost 1000 Japanese yen in 2005. The cost of ramen has increased by 0.5% per annum since then.
Determine the cost of the same bowl of ramen in 2020 in Japanese yen, to the nearest yen. (2 marks)
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`1078\ text{yen}`
`r =\ text(0.5%)\ = 0.005`
`n = 15\ text(years)`
| `FV` | `=PV(1+r)^n` | |
| `=1000(1 + 0.005)^15` | ||
| `=1077.68…` | ||
| `=1078\ text{yen}` |
At the pump, one litre of diesel fuel cost 98 cents in NSW in 2003. The value of diesel fuel has increased by 4% per annum since then.
Which expression gives the value, in cents, of one litre of diesel at the pump in 2023?
`B`
`r =\ text(4%)\ = 0.04`
`n = 20\ text(years)`
`text{Using}\ \ FV=PV(1+r)^n`
`text{Value in 2023} =98(1 + 0.04)^20`
`=> B`
A house was purchased in 1984 for $35 000. Assume that the value of the house has increased by 3% per annum since then.
Which expression gives the value of the house in 2009?
`A`
`r =\ text(3%)\ = 0.03`
`n = 25\ text(years)`
`text(Using)\ \ FV = PV(1 + r)^n`
` :.\ text(Value in 2009) = 35\ 000(1+0.03)^25`
`=> A`