Question:
Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10824
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 = $10824 – $6600 = $4224
Thus, Simple Interest = $4224
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 × 4224/6600 × 8
= 422400/52800
= 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) = $6600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4224 (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 $4224, then the time = 1/528 × 4224 years
= 1 × 4224/528 years
= 4224/528 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(2) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(4) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(9) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(10) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.