Question:
Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8476
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 = $8476 – $5200 = $3276
Thus, Simple Interest = $3276
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 × 3276/5200 × 9
= 327600/46800
= 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) = $5200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3276 (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 = 9% of Principal
= 9% of $5200
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = 468
Thus, simple Interest for 1 year = $468
Now,
∵ If the simple Interest is $468, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/468 years
∴ If the simple Interest is $3276, then the time = 1/468 × 3276 years
= 1 × 3276/468 years
= 3276/468 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(2) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(4) 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.
(5) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.