Question:
Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10758
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 = $10758 – $6600 = $4158
Thus, Simple Interest = $4158
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 × 4158/6600 × 9
= 415800/59400
= 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) = $6600
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4158 (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 = 9% of Principal
= 9% of $6600
= 9/100 × 6600
= 9 × 6600/100
= 59400/100 = 594
Thus, simple Interest for 1 year = $594
Now,
∵ If the simple Interest is $594, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/594 years
∴ If the simple Interest is $4158, then the time = 1/594 × 4158 years
= 1 × 4158/594 years
= 4158/594 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?