Question:
( 1 of 10 ) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
15
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11800
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 = $11800 – $5900 = $5900
Thus, Simple Interest = $5900
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 × 5900/5900 × 10
= 590000/59000
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5900 (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 = 10% of Principal
= 10% of $5900
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = 590
Thus, simple Interest for 1 year = $590
Now,
∵ If the simple Interest is $590, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/590 years
∴ If the simple Interest is $5900, then the time = 1/590 × 5900 years
= 1 × 5900/590 years
= 5900/590 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(3) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(5) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) 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.
(7) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.