Question:
Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7790
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 = $7790 – $4100 = $3690
Thus, Simple Interest = $3690
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 × 3690/4100 × 10
= 369000/41000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 10% per annum
Simple Interest = $3690 (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 $4100
= 10/100 × 4100
= 10 × 4100/100
= 41000/100 = 410
Thus, simple Interest for 1 year = $410
Now,
∵ If the simple Interest is $410, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/410 years
∴ If the simple Interest is $3690, then the time = 1/410 × 3690 years
= 1 × 3690/410 years
= 3690/410 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(2) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(4) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(6) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(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) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
(9) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.