Question:
Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9176
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 = $9176 – $6200 = $2976
Thus, Simple Interest = $2976
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 × 2976/6200 × 6
= 297600/37200
= 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) = $6200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2976 (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 $2976, then the time = 1/372 × 2976 years
= 1 × 2976/372 years
= 2976/372 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?
(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(4) 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.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(6) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(10) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.