Question:
Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9900
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 = $9900 – $5500 = $4400
Thus, Simple Interest = $4400
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 × 4400/5500 × 8
= 440000/44000
= 10 years (using formula)
Thus, Time (T) = 10 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) = 8% per annum
Simple Interest = $4400 (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 $5500
= 8/100 × 5500
= 8 × 5500/100
= 44000/100 = 440
Thus, simple Interest for 1 year = $440
Now,
∵ If the simple Interest is $440, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/440 years
∴ If the simple Interest is $4400, then the time = 1/440 × 4400 years
= 1 × 4400/440 years
= 4400/440 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(2) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.