To calculate the fortnightly installments for Martin's refrigerator, we need to determine the total amount he will repay over the 30 months, and then divide that by the number of installments.
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Identify the terms:
- Remaining balance (loan amount): K2500
- Interest rate: 10% per annum
- Time period: 30 months
- Fortnightly installments: 30 months × 2 = 60 installments
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Convert the annual interest rate to a fortnightly rate:
- The interest rate per year is 10%, so for a fortnightly period, we first find the fortnightly interest rate by dividing the annual interest rate by the number of fortnights in a year.
- There are 26 fortnights in a year (52 weeks / 2).
- Fortnightly interest rate = 10% / 26 ≈ 0.3846% per period
To use this in calculations, express this as a decimal: \[ \text{Fortnightly interest rate} = 0.003846 \]
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Calculate the fortnightly payment using the formula for an annuity: The formula for the payment \( P \) of an ordinary annuity is given by: \[ P = \frac{PV \cdot r}{1 - (1 + r)^{-n}} \] Where:
- \( PV \) = Present value (loan amount) = K2500
- \( r \) = Fortnightly interest rate = 0.003846
- \( n \) = Total number of payments = 60
Plugging in the values: \[ P = \frac{2500 \cdot 0.003846}{1 - (1 + 0.003846)^{-60}} \]
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Calculate \( (1 + r)^{-n} \): \[ (1 + 0.003846)^{-60} \approx (1.003846)^{-60} \approx 0.795776 \] Then, we can find \( 1 - (1 + r)^{-n} \): \[ 1 - 0.795776 \approx 0.204224 \]
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Now plug this back into the formula: \[ P \approx \frac{2500 \cdot 0.003846}{0.204224} \approx \frac{9.615}{0.204224} \approx 47.1 \]
Thus, the fortnightly installment that Martin needs to pay for his refrigerator is approximately K47.10.