Question:
Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9768
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 = $9768 – $6600 = $3168
Thus, Simple Interest = $3168
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 × 3168/6600 × 8
= 316800/52800
= 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) = $6600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3168 (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 $6600
= 8/100 × 6600
= 8 × 6600/100
= 52800/100 = 528
Thus, simple Interest for 1 year = $528
Now,
∵ If the simple Interest is $528, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/528 years
∴ If the simple Interest is $3168, then the time = 1/528 × 3168 years
= 1 × 3168/528 years
= 3168/528 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(8) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) 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.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.