Belinda borrowed $20,500 at simple interest rate of 4.30% p.a. from her parents to start a business. At the end of 3 months, she paid them $7,100 and $6,900 at the end of 8 months. How much would she have to pay them at the end of 18 months to clear the balance?
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To find out how much Belinda would have to pay at the end of 18 months to clear the balance, we need to calculate the accumulated interest on the loan over the entire duration.
First, let's calculate the interest accumulated during the first 3 months:
Interest1 = Principal * Rate * Time
Interest1 = $20,500 * 4.30% * (3/12) [converting 3 months to years]
Interest1 = $20,500 * 4.30% * 0.25
Interest1 = $221.75
The amount paid by Belinda at the end of 3 months is subtracted from the loan amount to calculate the remaining balance:
Balance1 = Principal + Interest1 - Payment1
Balance1 = $20,500 + $221.75 - $7,100
Balance1 = $13,621.75
Similarly, let's calculate the interest accumulated during the next 5 months (from 4th to 8th month):
Interest2 = Balance1 * Rate * Time
Interest2 = $13,621.75 * 4.30% * (5/12) [converting 5 months to years]
Interest2 = $13,621.75 * 4.30% * 0.42
Interest2 = $246.03
The amount paid by Belinda at the end of 8 months is subtracted from the remaining balance:
Balance2 = Balance1 + Interest2 - Payment2
Balance2 = $13,621.75 + $246.03 - $6,900
Balance2 = $6,967.78
Finally, let's calculate the interest accumulated during the remaining 10 months (from 9th to 18th month):
Interest3 = Balance2 * Rate * Time
Interest3 = $6,967.78 * 4.30% * (10/12) [converting 10 months to years]
Interest3 = $6,967.78 * 4.30% * 0.83
Interest3 = $239.28
To determine the total amount Belinda would have to pay at the end of 18 months, we add the remaining balance and the interest accumulated in the third period:
Total Payment = Balance2 + Interest3
Total Payment = $6,967.78 + $239.28
Total Payment = $7,207.06
Therefore, Belinda would have to pay $7,207.06 at the end of 18 months to clear the balance.