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) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(5) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(6) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.