Question:
Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6660
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 = $6660 – $4500 = $2160
Thus, Simple Interest = $2160
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 × 2160/4500 × 8
= 216000/36000
= 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) = $4500
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2160 (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 $4500
= 8/100 × 4500
= 8 × 4500/100
= 36000/100 = 360
Thus, simple Interest for 1 year = $360
Now,
∵ If the simple Interest is $360, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/360 years
∴ If the simple Interest is $2160, then the time = 1/360 × 2160 years
= 1 × 2160/360 years
= 2160/360 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.
(3) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(6) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.