Question:
Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7052
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 = $7052 – $4300 = $2752
Thus, Simple Interest = $2752
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 × 2752/4300 × 8
= 275200/34400
= 8 years (using formula)
Thus, Time (T) = 8 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 = $2752 (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 $2752, then the time = 1/344 × 2752 years
= 1 × 2752/344 years
= 2752/344 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.
(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(10) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.