Question:
( 1 of 10 ) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
12
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8772
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $8772 – $5100 = $3672
Thus, Simple Interest = $3672
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 3672/5100 × 9
= 367200/45900
= 8 years (using formula)
Thus, Time (T) = 8 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $5100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3672 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 9% of Principal
= 9% of $5100
= 9/100 × 5100
= 9 × 5100/100
= 45900/100 = 459
Thus, simple Interest for 1 year = $459
Now,
∵ If the simple Interest is $459, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/459 years
∴ If the simple Interest is $3672, then the time = 1/459 × 3672 years
= 1 × 3672/459 years
= 3672/459 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(4) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(6) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.