Question:
Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11590
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 = $11590 – $6100 = $5490
Thus, Simple Interest = $5490
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 × 5490/6100 × 10
= 549000/61000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 10% per annum
Simple Interest = $5490 (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 $6100
= 10/100 × 6100
= 10 × 6100/100
= 61000/100 = 610
Thus, simple Interest for 1 year = $610
Now,
∵ If the simple Interest is $610, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/610 years
∴ If the simple Interest is $5490, then the time = 1/610 × 5490 years
= 1 × 5490/610 years
= 5490/610 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(2) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?
(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(7) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(10) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.