A loan of rs. 12,300 at 5% per annum compound interest, is to be repaid in two equal annual installments at the end of every year. Find the amount of each installment?
Answers
Answer:
the amount of each installment = Rs 6615
Step-by-step explanation:
A loan of rs. 12,300 at 5% per annum compound interest, is to be repaid in two equal annual installments at the end of every year. Find the amount of each installment?
Principle to be paid = Rs 12300
Interest for 1st year at 5% = 12300 * 5 /100 = Rs 615
Let say equal annual installments = M
=> Principle Amount remained to be paid after 1 year = 12300 + 615 - M
= Rs 12915 - M
Interest for 2nd Year = ( 12915 - M) * 5 /100 = ( 12915 - M) /20
Total amount to be paid = Principle + 1st year interest + 2nd Year interest
= 12300 + 615 + ( 12915 - M) /20
Total amount paid = 2M ( two equal installments)
Equating Both
2M = 12300 + 615 + ( 12915 - M) /20
=> 40M = 20 ( 12915) + 12915 - M
=> 41M = 12915 ( 21)
=> M = 315 * 21
=> M = 6615
the amount of each installment = Rs 6615
Thus each installment is 6615 Rs.
Step-by-step explanation:
P = 12300 Rs
R = 5%
SI = P⋅R⋅T
5% = 1 / 20 = 21 → Installment / 20 → Principal
Year Principal Installment
⇒ I 20 × 21 → 21×21 ......(i)
⇒ II 400 → 441 .....(ii)
Since, installment is equal, hence multiply equation (i) by 21
⇒ Total principal = 420 + 400 = 820
⇒ 820 units = Rs. 12300
⇒ 1 units = Rs. 15
⇒ 441 units = Rs. 6615
∴ Each installment = Rs. 6615
Thus each installment is 6615 Rs.