Question:
Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9010
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 = $9010 – $5300 = $3710
Thus, Simple Interest = $3710
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 × 3710/5300 × 7
= 371000/37100
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3710 (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 $5300
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = 371
Thus, simple Interest for 1 year = $371
Now,
∵ If the simple Interest is $371, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/371 years
∴ If the simple Interest is $3710, then the time = 1/371 × 3710 years
= 1 × 3710/371 years
= 3710/371 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(7) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(8) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?
(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.