Question:
Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8460
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 = $8460 – $4700 = $3760
Thus, Simple Interest = $3760
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 × 3760/4700 × 8
= 376000/37600
= 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) = $4700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3760 (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 $3760, then the time = 1/376 × 3760 years
= 1 × 3760/376 years
= 3760/376 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(3) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(6) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(8) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.