Question:
Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 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) = 9% per annum
Amount (A) = $11780
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 = $11780 – $6200 = $5580
Thus, Simple Interest = $5580
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 × 5580/6200 × 9
= 558000/55800
= 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) = 9% per annum
Simple Interest = $5580 (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 = 9% of Principal
= 9% of $6200
= 9/100 × 6200
= 9 × 6200/100
= 55800/100 = 558
Thus, simple Interest for 1 year = $558
Now,
∵ If the simple Interest is $558, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/558 years
∴ If the simple Interest is $5580, then the time = 1/558 × 5580 years
= 1 × 5580/558 years
= 5580/558 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.
(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(5) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(10) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.