The value of a machine depreciates each year by 5% of its value at the beginning of that year. If its value when new on 1st January 1980 was 10250 naira what was its value in January 1989 when it was 9 years old
please show me the answers clear
To find the value of the machine in January 1989 when it was 9 years old, we need to calculate the depreciation of the machine each year.
The depreciation rate is given as 5% of its value at the beginning of each year.
Let's calculate the value of the machine each year, starting from 1980 until 1989:
Year 1980: Value = 10250 naira (New)
Year 1981: Value = 10250 - (5% of 10250) = 10250 - (0.05 * 10250) = 10250 - 512.5 = 9727.5 naira
Year 1982: Value = 9727.5 - (5% of 9727.5) = 9727.5 - (0.05 * 9727.5) = 9727.5 - 486.375 = 9241.125 naira
Year 1983: Value = 9241.125 - (5% of 9241.125) = 9241.125 - (0.05 * 9241.125) = 9241.125 - 462.05625 = 8779.06875 naira
Year 1984: Value = 8779.06875 - (5% of 8779.06875) = 8779.06875 - (0.05 * 8779.06875) = 8779.06875 - 438.9534375 = 8340.1153125 naira
Year 1985: Value = 8340.1153125 - (5% of 8340.1153125) = 8340.1153125 - (0.05 * 8340.1153125) = 8340.1153125 - 417.005765625 = 7923.109546875 naira
Year 1986: Value = 7923.109546875 - (5% of 7923.109546875) = 7923.109546875 - (0.05 * 7923.109546875) = 7923.109546875 - 396.15547734375 = 7526.95406953125 naira
Year 1987: Value = 7526.95406953125 - (5% of 7526.95406953125) = 7526.95406953125 - (0.05 * 7526.95406953125) = 7526.95406953125 - 376.347703476563 = 7150.60636605469 naira
Year 1988: Value = 7150.60636605469 - (5% of 7150.60636605469) = 7150.60636605469 - (0.05 * 7150.60636605469) = 7150.60636605469 - 357.530318302734 = 6793.07604775195 naira
Year 1989: Value = 6793.07604775195 - (5% of 6793.07604775195) = 6793.07604775195 - (0.05 * 6793.07604775195) = 6793.07604775195 - 339.653802387598 = 6453.42224536435 naira
Therefore, the value of the machine in January 1989 when it was 9 years old was approximately 6453.42 naira.
To find the value of the machine in January 1989, we will apply the depreciation rate of 5% per year for each of the 9 years.
1. Calculate the depreciation per year:
Depreciation per year = 5% of the value at the beginning of the year
= 5/100 * 10250 naira (value in January 1980)
= 512.50 naira per year
2. Calculate the value of the machine at the beginning of each year from 1981 to 1989:
Year 1980: 10250 naira (given)
Year 1981: 10250 - 512.50 = 9700 naira
Year 1982: 9700 - 512.50 = 9187.50 naira
Year 1983: 9187.50 - 512.50 = 8675 naira
Year 1984: 8675 - 512.50 = 8162.50 naira
Year 1985: 8162.50 - 512.50 = 7650 naira
Year 1986: 7650 - 512.50 = 7137.50 naira
Year 1987: 7137.50 - 512.50 = 6625 naira
Year 1988: 6625 - 512.50 = 6112.50 naira
Year 1989: 6112.50 - 512.50 = 5600 naira
Therefore, the value of the machine in January 1989 when it was 9 years old was 5600 naira.
It retains 95% of its value each year,
so for each year of service, multiply by another 0.95
what do you think?