Question:
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.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6622
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 = $6622 – $4300 = $2322
Thus, Simple Interest = $2322
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 × 2322/4300 × 6
= 232200/25800
= 9 years (using formula)
Thus, Time (T) = 9 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 = $2322 (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 $2322, then the time = 1/258 × 2322 years
= 1 × 2322/258 years
= 2322/258 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(8) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.