Question:
Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10010
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 = $10010 – $6500 = $3510
Thus, Simple Interest = $3510
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 × 3510/6500 × 9
= 351000/58500
= 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) = $6500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3510 (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 $6500
= 9/100 × 6500
= 9 × 6500/100
= 58500/100 = 585
Thus, simple Interest for 1 year = $585
Now,
∵ If the simple Interest is $585, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/585 years
∴ If the simple Interest is $3510, then the time = 1/585 × 3510 years
= 1 × 3510/585 years
= 3510/585 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?