Question:
Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9394
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 = $9394 – $6100 = $3294
Thus, Simple Interest = $3294
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 × 3294/6100 × 9
= 329400/54900
= 6 years (using formula)
Thus, Time (T) = 6 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) = $6100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3294 (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 = 9% of Principal
= 9% of $6100
= 9/100 × 6100
= 9 × 6100/100
= 54900/100 = 549
Thus, simple Interest for 1 year = $549
Now,
∵ If the simple Interest is $549, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/549 years
∴ If the simple Interest is $3294, then the time = 1/549 × 3294 years
= 1 × 3294/549 years
= 3294/549 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.