Question:
Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8692
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 = $8692 – $5300 = $3392
Thus, Simple Interest = $3392
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 × 3392/5300 × 8
= 339200/42400
= 8 years (using formula)
Thus, Time (T) = 8 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) = 8% per annum
Simple Interest = $3392 (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 = 8% of Principal
= 8% of $5300
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = 424
Thus, simple Interest for 1 year = $424
Now,
∵ If the simple Interest is $424, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/424 years
∴ If the simple Interest is $3392, then the time = 1/424 × 3392 years
= 1 × 3392/424 years
= 3392/424 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(3) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(4) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(7) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(9) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.