Question:
Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8268
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 = $8268 – $5300 = $2968
Thus, Simple Interest = $2968
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 × 2968/5300 × 7
= 296800/37100
= 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) = $5300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2968 (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 $5300
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = 371
Thus, simple Interest for 1 year = $371
Now,
∵ If the simple Interest is $371, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/371 years
∴ If the simple Interest is $2968, then the time = 1/371 × 2968 years
= 1 × 2968/371 years
= 2968/371 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(6) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.