Question:
Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8140
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 = $8140 – $5500 = $2640
Thus, Simple Interest = $2640
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 × 2640/5500 × 6
= 264000/33000
= 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) = $5500
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2640 (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 $5500
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = 330
Thus, simple Interest for 1 year = $330
Now,
∵ If the simple Interest is $330, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/330 years
∴ If the simple Interest is $2640, then the time = 1/330 × 2640 years
= 1 × 2640/330 years
= 2640/330 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(3) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(8) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(9) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?