Question:
Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10540
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 = $10540 – $6200 = $4340
Thus, Simple Interest = $4340
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 × 4340/6200 × 10
= 434000/62000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $6200
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4340 (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 $6200
= 10/100 × 6200
= 10 × 6200/100
= 62000/100 = 620
Thus, simple Interest for 1 year = $620
Now,
∵ If the simple Interest is $620, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/620 years
∴ If the simple Interest is $4340, then the time = 1/620 × 4340 years
= 1 × 4340/620 years
= 4340/620 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(10) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.