Question:
Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8436
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 = $8436 – $5700 = $2736
Thus, Simple Interest = $2736
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 × 2736/5700 × 8
= 273600/45600
= 6 years (using formula)
Thus, Time (T) = 6 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 = $2736 (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 $2736, then the time = 1/456 × 2736 years
= 1 × 2736/456 years
= 2736/456 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(2) 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.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(6) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(8) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?