Question:
Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $6314
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 = $6314 – $4100 = $2214
Thus, Simple Interest = $2214
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 × 2214/4100 × 9
= 221400/36900
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2214 (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 $4100
= 9/100 × 4100
= 9 × 4100/100
= 36900/100 = 369
Thus, simple Interest for 1 year = $369
Now,
∵ If the simple Interest is $369, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/369 years
∴ If the simple Interest is $2214, then the time = 1/369 × 2214 years
= 1 × 2214/369 years
= 2214/369 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(7) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(10) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.