Question:
Charles took a loan of $5800 at the rate of 9% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 9% 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 × 9
= 365400/52200
= 7 years (using formula)
Thus, Time (T) = 7 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) = 9% 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 = 9% of Principal
= 9% of $5800
= 9/100 × 5800
= 9 × 5800/100
= 52200/100 = 522
Thus, simple Interest for 1 year = $522
Now,
∵ If the simple Interest is $522, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/522 years
∴ If the simple Interest is $3654, then the time = 1/522 × 3654 years
= 1 × 3654/522 years
= 3654/522 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(3) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(5) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?