Question:
Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10921
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 = $10921 – $6700 = $4221
Thus, Simple Interest = $4221
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 × 4221/6700 × 7
= 422100/46900
= 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) = $6700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4221 (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 = 7% of Principal
= 7% of $6700
= 7/100 × 6700
= 7 × 6700/100
= 46900/100 = 469
Thus, simple Interest for 1 year = $469
Now,
∵ If the simple Interest is $469, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/469 years
∴ If the simple Interest is $4221, then the time = 1/469 × 4221 years
= 1 × 4221/469 years
= 4221/469 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(2) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(4) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(7) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.
(10) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.