Question:
Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9454
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 = $9454 – $5800 = $3654
Thus, Simple Interest = $3654
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 × 3654/5800 × 7
= 365400/40600
= 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) = $5800
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3654 (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 $5800
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = 406
Thus, simple Interest for 1 year = $406
Now,
∵ If the simple Interest is $406, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/406 years
∴ If the simple Interest is $3654, then the time = 1/406 × 3654 years
= 1 × 3654/406 years
= 3654/406 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.