Question:
Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9350
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 = $9350 – $5500 = $3850
Thus, Simple Interest = $3850
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 × 3850/5500 × 10
= 385000/55000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $5500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3850 (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 = 10% of Principal
= 10% of $5500
= 10/100 × 5500
= 10 × 5500/100
= 55000/100 = 550
Thus, simple Interest for 1 year = $550
Now,
∵ If the simple Interest is $550, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/550 years
∴ If the simple Interest is $3850, then the time = 1/550 × 3850 years
= 1 × 3850/550 years
= 3850/550 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(4) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(6) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(8) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?
(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.