Question:
Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7844
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 = $7844 – $5300 = $2544
Thus, Simple Interest = $2544
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 × 2544/5300 × 8
= 254400/42400
= 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) = $5300
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2544 (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 $5300
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = 424
Thus, simple Interest for 1 year = $424
Now,
∵ If the simple Interest is $424, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/424 years
∴ If the simple Interest is $2544, then the time = 1/424 × 2544 years
= 1 × 2544/424 years
= 2544/424 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(2) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(6) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.