Question:
Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $13110
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 = $13110 – $6900 = $6210
Thus, Simple Interest = $6210
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 × 6210/6900 × 10
= 621000/69000
= 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) = $6900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6210 (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 $6900
= 10/100 × 6900
= 10 × 6900/100
= 69000/100 = 690
Thus, simple Interest for 1 year = $690
Now,
∵ If the simple Interest is $690, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/690 years
∴ If the simple Interest is $6210, then the time = 1/690 × 6210 years
= 1 × 6210/690 years
= 6210/690 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
(7) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(8) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(9) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
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