Question:
( 2 of 10 ) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(A) 154 1/11% या 154.09%
(B) 309 1/11% या 309.09%
(C) 618 1/11% या 618.09%
(D) 927 1/11% या 927.09%
You selected
15
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10400
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 = $10400 – $5200 = $5200
Thus, Simple Interest = $5200
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 × 5200/5200 × 10
= 520000/52000
= 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) = $5200
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5200 (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 $5200
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = 520
Thus, simple Interest for 1 year = $520
Now,
∵ If the simple Interest is $520, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/520 years
∴ If the simple Interest is $5200, then the time = 1/520 × 5200 years
= 1 × 5200/520 years
= 5200/520 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.