A tractor bought for R120 000 depreciates to R11 090,41 after 12 years by using the reducing balance method. Calculate the rate of depreciation per annum if the rate was fixed over the 12 years, and calculate the effective interest rate if interest is 9,8% p.a., compounded monthly.
P = Po - Po*r*t = 11,090.41
120,000 - 120,000*r*12 = 11,090.41
-1,440,000r = 11,090.41 - 120,000
r = 0.0756 = 7.56% per annum
To calculate the rate of depreciation per annum, we can use the following formula:
Rate of depreciation = (Initial value - Final value) / Number of years
In this case, the initial value is R120,000, the final value is R11,090.41, and the number of years is 12.
Rate of depreciation = (120,000 - 11,090.41) / 12
= 108,909.59 / 12
= R9,075.80 per annum
The rate of depreciation per annum is R9,075.80.
To calculate the effective interest rate if interest is 9.8% p.a., compounded monthly, we can use the formula for compound interest:
Future value = Present value * (1 + Interest rate / Number of compounding periods)^(Number of compounding periods * Number of years)
In this case, the present value is R11,090.41, the interest rate is 9.8% (or 0.098), and the number of compounding periods per year is 12. The number of years is also 12.
Future value = 11,090.41 * (1 + 0.098 / 12)^(12 * 12)
= 11,090.41 * (1 + 0.008167)^144
= 11,090.41 * (1.008167)^144
= 11,090.41 * 2.992705
= R33,324.73
The future value of the tractor after 12 years with an effective interest rate of 9.8% p.a., compounded monthly, is R33,324.73.
To calculate the rate of depreciation per annum, we can use the formula:
Rate of depreciation per annum = (Initial value - Final value) / Initial value / Number of years
In this case, the initial value of the tractor is R120,000, and the final value is R11,090.41. The number of years is 12. Plugging these values into the formula, we get:
Rate of depreciation per annum = (120000 - 11090.41) / 120000 / 12
Calculating this, we get:
Rate of depreciation per annum = 0.072
So, the rate of depreciation per annum is 0.072, or 7.2%.
To calculate the effective interest rate if interest is 9.8% p.a., compounded monthly, we can use the formula for compound interest:
A = P * (1 + r/n) ^ (n*t)
In this formula, A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal amount is R1 (as we are only interested in the interest rate), the annual interest rate is 9.8%, compounded monthly, so n is 12, and the number of years is 1.
Plugging these values into the formula, we get:
A = 1 * (1 + 0.098/12)^(12*1)
Calculating this, we get:
A = 1.0983
So, the final amount after one year with an annual interest rate of 9.8% compounded monthly is 1.0983.
To calculate the effective interest rate, we subtract 1 from this amount:
Effective interest rate = A - 1 = 1.0983 - 1
Calculating this, we get:
Effective interest rate = 0.0983
So, the effective interest rate is 0.0983, or 9.83%.