Question:
Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9834
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 = $9834 – $6600 = $3234
Thus, Simple Interest = $3234
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 × 3234/6600 × 7
= 323400/46200
= 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) = $6600
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3234 (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 $6600
= 7/100 × 6600
= 7 × 6600/100
= 46200/100 = 462
Thus, simple Interest for 1 year = $462
Now,
∵ If the simple Interest is $462, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/462 years
∴ If the simple Interest is $3234, then the time = 1/462 × 3234 years
= 1 × 3234/462 years
= 3234/462 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(5) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(6) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(7) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(8) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.