Question:
Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9540
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 = $9540 – $5300 = $4240
Thus, Simple Interest = $4240
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 × 4240/5300 × 10
= 424000/53000
= 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) = $5300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4240 (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 = 10% of Principal
= 10% of $5300
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = 530
Thus, simple Interest for 1 year = $530
Now,
∵ If the simple Interest is $530, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/530 years
∴ If the simple Interest is $4240, then the time = 1/530 × 4240 years
= 1 × 4240/530 years
= 4240/530 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(6) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(7) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(9) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.