Question:
Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9760
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 = $9760 – $6100 = $3660
Thus, Simple Interest = $3660
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 × 3660/6100 × 6
= 366000/36600
= 10 years (using formula)
Thus, Time (T) = 10 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) = 6% per annum
Simple Interest = $3660 (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 = 6% of Principal
= 6% of $6100
= 6/100 × 6100
= 6 × 6100/100
= 36600/100 = 366
Thus, simple Interest for 1 year = $366
Now,
∵ If the simple Interest is $366, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/366 years
∴ If the simple Interest is $3660, then the time = 1/366 × 3660 years
= 1 × 3660/366 years
= 3660/366 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(4) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(6) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.