Question:
Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9920
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 = $9920 – $6200 = $3720
Thus, Simple Interest = $3720
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 × 3720/6200 × 6
= 372000/37200
= 10 years (using formula)
Thus, Time (T) = 10 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) = 6% per annum
Simple Interest = $3720 (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 = 6% of Principal
= 6% of $6200
= 6/100 × 6200
= 6 × 6200/100
= 37200/100 = 372
Thus, simple Interest for 1 year = $372
Now,
∵ If the simple Interest is $372, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/372 years
∴ If the simple Interest is $3720, then the time = 1/372 × 3720 years
= 1 × 3720/372 years
= 3720/372 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
(2) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(7) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(10) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.