Question:
Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 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) = 6% per annum
Amount (A) = $7526
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 = $7526 – $5300 = $2226
Thus, Simple Interest = $2226
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 × 2226/5300 × 6
= 222600/31800
= 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) = 6% per annum
Simple Interest = $2226 (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 = 6% of Principal
= 6% of $5300
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = 318
Thus, simple Interest for 1 year = $318
Now,
∵ If the simple Interest is $318, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/318 years
∴ If the simple Interest is $2226, then the time = 1/318 × 2226 years
= 1 × 2226/318 years
= 2226/318 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(7) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(8) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(9) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.