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) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(7) Betty took a loan of $6500 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.
(8) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(10) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.