Question:
Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7708
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 = $7708 – $4700 = $3008
Thus, Simple Interest = $3008
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 × 3008/4700 × 8
= 300800/37600
= 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) = $4700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3008 (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 = 8% of Principal
= 8% of $4700
= 8/100 × 4700
= 8 × 4700/100
= 37600/100 = 376
Thus, simple Interest for 1 year = $376
Now,
∵ If the simple Interest is $376, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/376 years
∴ If the simple Interest is $3008, then the time = 1/376 × 3008 years
= 1 × 3008/376 years
= 3008/376 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(2) 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.
(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.