Question:
Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8316
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 = $8316 – $5400 = $2916
Thus, Simple Interest = $2916
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 × 2916/5400 × 6
= 291600/32400
= 9 years (using formula)
Thus, Time (T) = 9 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) = $5400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2916 (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 = 6% of Principal
= 6% of $5400
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = 324
Thus, simple Interest for 1 year = $324
Now,
∵ If the simple Interest is $324, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/324 years
∴ If the simple Interest is $2916, then the time = 1/324 × 2916 years
= 1 × 2916/324 years
= 2916/324 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(4) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(7) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(8) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.