Question:
( 1 of 10 ) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(A) 14.575 meter
(B) 21 meter
(C) 36.4375 meter
(D) 29.15 meter
You selected
15
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12200
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 = $12200 – $6100 = $6100
Thus, Simple Interest = $6100
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 × 6100/6100 × 10
= 610000/61000
= 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) = $6100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6100 (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 $6100
= 10/100 × 6100
= 10 × 6100/100
= 61000/100 = 610
Thus, simple Interest for 1 year = $610
Now,
∵ If the simple Interest is $610, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/610 years
∴ If the simple Interest is $6100, then the time = 1/610 × 6100 years
= 1 × 6100/610 years
= 6100/610 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(3) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(6) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(8) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.