Question:
Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6708
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 = $6708 – $4300 = $2408
Thus, Simple Interest = $2408
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 × 2408/4300 × 8
= 240800/34400
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4300
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2408 (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 $4300
= 8/100 × 4300
= 8 × 4300/100
= 34400/100 = 344
Thus, simple Interest for 1 year = $344
Now,
∵ If the simple Interest is $344, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/344 years
∴ If the simple Interest is $2408, then the time = 1/344 × 2408 years
= 1 × 2408/344 years
= 2408/344 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(5) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(7) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(8) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
(9) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.