Question:
Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9348
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 = $9348 – $5700 = $3648
Thus, Simple Interest = $3648
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 × 3648/5700 × 8
= 364800/45600
= 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) = $5700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3648 (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 $5700
= 8/100 × 5700
= 8 × 5700/100
= 45600/100 = 456
Thus, simple Interest for 1 year = $456
Now,
∵ If the simple Interest is $456, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/456 years
∴ If the simple Interest is $3648, then the time = 1/456 × 3648 years
= 1 × 3648/456 years
= 3648/456 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(4) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(6) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(9) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(10) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.