Question:
Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $5848
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 = $5848 – $4300 = $1548
Thus, Simple Interest = $1548
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 × 1548/4300 × 6
= 154800/25800
= 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) = $4300
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1548 (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 = 6% of Principal
= 6% of $4300
= 6/100 × 4300
= 6 × 4300/100
= 25800/100 = 258
Thus, simple Interest for 1 year = $258
Now,
∵ If the simple Interest is $258, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/258 years
∴ If the simple Interest is $1548, then the time = 1/258 × 1548 years
= 1 × 1548/258 years
= 1548/258 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(6) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(8) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
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