Question:
Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 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) = 6% per annum
Amount (A) = $6106
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 = $6106 – $4300 = $1806
Thus, Simple Interest = $1806
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 × 1806/4300 × 6
= 180600/25800
= 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) = 6% per annum
Simple Interest = $1806 (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 $1806, then the time = 1/258 × 1806 years
= 1 × 1806/258 years
= 1806/258 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(3) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.