Question:
Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9943
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 = $9943 – $6100 = $3843
Thus, Simple Interest = $3843
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 × 3843/6100 × 9
= 384300/54900
= 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) = $6100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3843 (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 $3843, then the time = 1/549 × 3843 years
= 1 × 3843/549 years
= 3843/549 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(2) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(6) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.
(10) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.