Question:
Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7661
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 = $7661 – $4700 = $2961
Thus, Simple Interest = $2961
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 × 2961/4700 × 7
= 296100/32900
= 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) = $4700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2961 (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 = 7% of Principal
= 7% of $4700
= 7/100 × 4700
= 7 × 4700/100
= 32900/100 = 329
Thus, simple Interest for 1 year = $329
Now,
∵ If the simple Interest is $329, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/329 years
∴ If the simple Interest is $2961, then the time = 1/329 × 2961 years
= 1 × 2961/329 years
= 2961/329 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(2) 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.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(6) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.