Question:
Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10880
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 = $10880 – $6800 = $4080
Thus, Simple Interest = $4080
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 × 4080/6800 × 10
= 408000/68000
= 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) = $6800
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4080 (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 $6800
= 10/100 × 6800
= 10 × 6800/100
= 68000/100 = 680
Thus, simple Interest for 1 year = $680
Now,
∵ If the simple Interest is $680, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/680 years
∴ If the simple Interest is $4080, then the time = 1/680 × 4080 years
= 1 × 4080/680 years
= 4080/680 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(2) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(6) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.