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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]
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): тВ╣30,000
Rate (R): 12% per annum
Time (T): 2 years
Interest (I) after 2 years:
ЁЭР╝
=
ЁЭСГ
├Ч
ЁЭСЕ
├Ч
ЁЭСЗ
=
30000
├Ч
12
100
├Ч
2
=
тВ╣
7200
I=P├ЧR├ЧT=30000├Ч
100
12
тАЛ
├Ч2=тВ╣7200
Total amount due after 2 years:
Total┬аAmount
=
ЁЭСГ
ЁЭСЯ
ЁЭСЦ
ЁЭСЫ
ЁЭСР
ЁЭСЦ
ЁЭСЭ
ЁЭСО
ЁЭСЩ
+
ЁЭР╝
ЁЭСЫ
ЁЭСб
ЁЭСТ
ЁЭСЯ
ЁЭСТ
ЁЭСа
ЁЭСб
=
30000
+
7200
=
тВ╣
37200
Total┬аAmount=Principal+Interest=30000+7200=тВ╣37200
After paying тВ╣15,200, the outstanding balance is:
Outstanding┬аBalance
=
37200
тИТ
15200
=
тВ╣
22000
Outstanding┬аBalance=37200тИТ15200=тВ╣22000
Now, for the next 2 years, calculate the interest on the remaining balance:
Interest┬аfor┬а2┬аmore┬аyears
=
22000
├Ч
12
100
├Ч
2
=
тВ╣
5280
Interest┬аfor┬а2┬аmore┬аyears=22000├Ч
100
12
тАЛ
├Ч2=тВ╣5280
Total amount to clear the loan after 2 more years:
Total
=
22000
+
5280
=
тВ╣
27280
Total=22000+5280=тВ╣27280
Thus, he will have to pay тВ╣27,280 to clear the loan.