A man took out a 30,000 loan from a bank at a simple interest rate of 12% annually. After two years, he gave the bank $15,200. How much will he have to pay to repay the loan in two more years? [Answer Limit: 125 words] [UKPSC 2012]
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To find out how much the man will have to pay after two more years, we first calculate the simple interest for the initial two years.
Principal (P): ₹30,000
Rate (R): 12% per annum
Time (T): 2 years
Interest (I) after 2 years:
𝐼
=
𝑃
×
𝑅
×
𝑇
=
30000
×
12
100
×
2
=
₹
7200
I=P×R×T=30000×
100
12
×2=₹7200
Total amount due after 2 years:
Total Amount
=
𝑃
𝑟
𝑖
𝑛
𝑐
𝑖
𝑝
𝑎
𝑙
+
𝐼
𝑛
𝑡
𝑒
𝑟
𝑒
𝑠
𝑡
=
30000
+
7200
=
₹
37200
Total Amount=Principal+Interest=30000+7200=₹37200
After paying ₹15,200, the outstanding balance is:
Outstanding Balance
=
37200
−
15200
=
₹
22000
Outstanding Balance=37200−15200=₹22000
Now, for the next 2 years, calculate the interest on the remaining balance:
Interest for 2 more years
=
22000
×
12
100
×
2
=
₹
5280
Interest for 2 more years=22000×
100
12
×2=₹5280
Total amount to clear the loan after 2 more years:
Total
=
22000
+
5280
=
₹
27280
Total=22000+5280=₹27280
Thus, he will have to pay ₹27,280 to clear the loan.