Question:
Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10492
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 = $10492 – $6100 = $4392
Thus, Simple Interest = $4392
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 × 4392/6100 × 9
= 439200/54900
= 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) = $6100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4392 (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 $4392, then the time = 1/549 × 4392 years
= 1 × 4392/549 years
= 4392/549 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(2) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(6) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?
(7) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.