Question:
Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8944
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 = $8944 – $5200 = $3744
Thus, Simple Interest = $3744
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 × 3744/5200 × 8
= 374400/41600
= 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) = $5200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3744 (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 $5200
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = 416
Thus, simple Interest for 1 year = $416
Now,
∵ If the simple Interest is $416, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/416 years
∴ If the simple Interest is $3744, then the time = 1/416 × 3744 years
= 1 × 3744/416 years
= 3744/416 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?
(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(5) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(10) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.