To calculate the fortnightly installment amount for Martin's refrigerator, we need to account for the details of the loan: a principal amount of K2500, an interest rate of 10% per annum, and a repayment period of 30 months.
Step 1: Convert the Annual Interest Rate to Fortnightly
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Annual interest rate (r): 10% or 0.10
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Fortnightly interest rate:
\[ r_{fortnightly} = \frac{0.10}{26} \approx 0.003846 \]
(There are 26 fortnights in a year).
Step 2: Calculate the Total Number of Payments
- Total periods (n): 30 months × 2 = 60 fortnights
Step 3: Use the Formula for the Installment Payment
To determine the installment payment (PMT), we can use the loan payment formula:
\[ PMT = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \(PMT\) = payment per period
- \(P\) = principal (loan amount) = K2500
- \(r\) = interest rate per period (fortnightly) = 0.003846
- \(n\) = total number of payments = 60
Step 4: Calculate PMT
Plugging in the values, we get:
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Calculate \((1 + r)^n\):
\[ (1 + 0.003846)^{60} \approx 1.28368 \]
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Now, substituting into the formula:
\[ PMT = 2500 \times \frac{0.003846 \times 1.28368}{1.28368 - 1} \]
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Calculate the numerator:
\[ 0.003846 \times 1.28368 \approx 0.004938 \]
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Calculate the denominator:
\[ 1.28368 - 1 \approx 0.28368 \]
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Now substitute these values back into the PMT formula:
\[ PMT = 2500 \times \frac{0.004938}{0.28368} \approx 2500 \times 0.0174 \approx 43.50 \]
Result:
The fortnightly installment payment that Martin will need to make for the refrigerator is approximately K43.50.
Conclusion:
Martin will pay about K43.50 every fortnight for 30 months to cover the K2500 balance for the refrigerator at a 10% annual interest rate.