Question:
Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9780
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 = $9780 – $6000 = $3780
Thus, Simple Interest = $3780
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 × 3780/6000 × 7
= 378000/42000
= 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) = $6000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3780 (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 = 7% of Principal
= 7% of $6000
= 7/100 × 6000
= 7 × 6000/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $3780, then the time = 1/420 × 3780 years
= 1 × 3780/420 years
= 3780/420 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(2) 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.
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.