To calculate the fortnightly installments for the remaining balance of K2500 at an interest rate of 10% per annum over 30 months, we can use the formula for the payment of an installment loan.
First, let's break down the components needed for the calculation:
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Principal Amount (Loan Amount): K2500
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Annual Interest Rate (r): 10% or 0.10
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Number of Fortnightly Payments (n): Since there are 30 months and payments are made fortnightly:
- 30 months = 30 x 2 = 60 fortnights.
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Fortnightly Interest Rate (i): Since the interest rate is annual, we need to convert it to a fortnightly rate: \[ i = \frac{0.10}{26} \approx 0.00384615 \]
Now, we can use the formula for the payment of an installment loan, which is given by: \[ PMT = \frac{P \cdot i}{1 - (1 + i)^{-n}} \] Where:
- \( PMT \) = periodic payment (fortnightly installment)
- \( P \) = principal amount (K2500)
- \( i \) = interest rate per period (fortnightly interest rate)
- \( n \) = number of payments (60 fortnights)
Substituting the values into the formula: \[ PMT = \frac{2500 \cdot 0.00384615}{1 - (1 + 0.00384615)^{-60}} \]
Calculating the denominator: \[ 1 + i = 1 + 0.00384615 \approx 1.00384615 \] \[ (1 + i)^{-n} = (1.00384615)^{-60} \approx 0.78086567 \] \[ 1 - (1 + i)^{-n} \approx 1 - 0.78086567 \approx 0.21913433 \]
Now substituting back into the payment formula: \[ PMT = \frac{2500 \cdot 0.00384615}{0.21913433} \approx \frac{9.615375}{0.21913433} \approx 43.88 \]
Fortnightly Installment: The fortnightly installment is approximately K43.88.
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