Question:
Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 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) = 10% per annum
Amount (A) = $11220
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 = $11220 – $6600 = $4620
Thus, Simple Interest = $4620
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 × 4620/6600 × 10
= 462000/66000
= 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) = 10% per annum
Simple Interest = $4620 (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 = 10% of Principal
= 10% of $6600
= 10/100 × 6600
= 10 × 6600/100
= 66000/100 = 660
Thus, simple Interest for 1 year = $660
Now,
∵ If the simple Interest is $660, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/660 years
∴ If the simple Interest is $4620, then the time = 1/660 × 4620 years
= 1 × 4620/660 years
= 4620/660 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.