Question:
Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10980
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 = $10980 – $6100 = $4880
Thus, Simple Interest = $4880
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 × 4880/6100 × 10
= 488000/61000
= 8 years (using formula)
Thus, Time (T) = 8 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 = $4880 (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 $4880, then the time = 1/610 × 4880 years
= 1 × 4880/610 years
= 4880/610 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(7) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.