A bank offered a unique loan to Abhay of 10 years, wherein the rate of interest for the first 2 years is 8%, that for the next 5 years is 12%, and that for beyond 7 years is 15%. If the amount that Abhay paid back to the bank was 1,87,850 in total, then the amount that he received as loan was:
a- 95k
b-85k
c-84.56k
d-93k
Answers
Solution :-
Let us assume that, the amount received as loan was Rs. 100x .
Case 1) :-
→ Principal = Rs. 100x
→ Time = 2 years
→ Rate = 8% per annum
So,
→ Simple interest = (Principal * rate * time)/100 = (100x * 2 * 8)/100 = Rs. 16x
then,
→ Amount paid back to the bank = Principal + simple interest = 100x + 16x = Rs. 116x
Case 2) :-
→ Principal = Rs. 100x
→ Time = 5 years
→ Rate = 12% per annum
So,
→ Simple interest = (Principal * rate * time)/100 = (100x * 12 * 5)/100 = Rs. 60x
then,
→ Amount paid back to the bank = Principal + simple interest = 100x + 60x = Rs. 160x
Case 3) :-
→ Principal = Rs. 100x
→ Time = 10 - 7 = 3 years
→ Rate = 15% per annum
So,
→ Simple interest = (Principal * rate * time)/100 = (100x * 3 * 15)/100 = Rs. 45x
then,
→ Amount paid back to the bank = Principal + simple interest = 100x + 45x = Rs. 145x
adding all we get,
→ Total amount paid back = Rs.187850
→ 116x + 160x + 145x = 187850
→ 421x = 187850
→ x = 446.199
therefore,
→ Amount recieved as a loan = 446.199 * 100 = 44619.9 ≈ Rs. 46620 = (46620/1000) = 46.62 k [ 1k = Rs. 1000. ]
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Amount received as loan was 85k if 1,87,850 was paid back after 10 years for interest rate for first 2 years as 8%, for the next 5 years as 12% and for beyond 7 years as 15%.
Step-by-step explanation:
Given:
- Time period of loan is 10 years
- Interest for 2 years is 8 %
- interest for next 5 years is 12%
- Amount Paid back is 187850
To Find:
- Amount of Loan taken
Solution:
- Considering Simple interest
- Formula for simple interest
- SI = P * R * T/100
- P = Principal
- R = Rate of interest
- T = Time
- SI = Simple Interest
Step 1:
Assume Loan amount taken = 100x
Step 2:
Calculate interest for first 2 years
= 100x * 8 * 2/100
= 16x
Step 3:
Calculate interest for next 5 years
= 100x * 12 * 5/100
= 60x
Step 4:
Calculate interest for remaining (10 - 7) 3 years
= 100x * 15 * 3/100
= 45x
Step 5:
Find loan amount to be repaid by adding loan taken and all the interest
100x + 16x + 60x + 45x = 221x
Step 6:
Equate with 187850 and solve for x and hence find 100x
221x = 187850
=> x = 850
=> 100x = 85000
Step 7:
Divide 85000 by 1000 to convert in k (thousands)
85000 = 85k
Hence amount received as loan was 85k
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