Question:
Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11390
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 = $11390 – $6700 = $4690
Thus, Simple Interest = $4690
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 × 4690/6700 × 10
= 469000/67000
= 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) = $6700
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4690 (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 $6700
= 10/100 × 6700
= 10 × 6700/100
= 67000/100 = 670
Thus, simple Interest for 1 year = $670
Now,
∵ If the simple Interest is $670, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/670 years
∴ If the simple Interest is $4690, then the time = 1/670 × 4690 years
= 1 × 4690/670 years
= 4690/670 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(2) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(4) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.