Question:
Lisa took a loan of $6100 at the rate of 10% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 10% 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 × 10
= 366000/61000
= 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) = 10% 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 = 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 $3660, then the time = 1/610 × 3660 years
= 1 × 3660/610 years
= 3660/610 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?