Question:
Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9880
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 = $9880 – $5200 = $4680
Thus, Simple Interest = $4680
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 × 4680/5200 × 10
= 468000/52000
= 9 years (using formula)
Thus, Time (T) = 9 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 = $4680 (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 $4680, then the time = 1/520 × 4680 years
= 1 × 4680/520 years
= 4680/520 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(4) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(5) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.