Question:
Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 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) = 9% per annum
Amount (A) = $11041
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 = $11041 – $6100 = $4941
Thus, Simple Interest = $4941
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 × 4941/6100 × 9
= 494100/54900
= 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) = 9% per annum
Simple Interest = $4941 (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 $4941, then the time = 1/549 × 4941 years
= 1 × 4941/549 years
= 4941/549 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(10) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?