Question:
Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8639
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 = $8639 – $5300 = $3339
Thus, Simple Interest = $3339
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 × 3339/5300 × 9
= 333900/47700
= 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) = $5300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3339 (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 $5300
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = 477
Thus, simple Interest for 1 year = $477
Now,
∵ If the simple Interest is $477, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/477 years
∴ If the simple Interest is $3339, then the time = 1/477 × 3339 years
= 1 × 3339/477 years
= 3339/477 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(7) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(10) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?