Question:
Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 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) = 7% per annum
Amount (A) = $8892
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 = $8892 – $5700 = $3192
Thus, Simple Interest = $3192
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 × 3192/5700 × 7
= 319200/39900
= 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) = 7% per annum
Simple Interest = $3192 (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 = 7% of Principal
= 7% of $5700
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = 399
Thus, simple Interest for 1 year = $399
Now,
∵ If the simple Interest is $399, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/399 years
∴ If the simple Interest is $3192, then the time = 1/399 × 3192 years
= 1 × 3192/399 years
= 3192/399 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(7) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.