Question:
John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8360
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 = $8360 – $4400 = $3960
Thus, Simple Interest = $3960
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 × 3960/4400 × 9
= 396000/39600
= 10 years (using formula)
Thus, Time (T) = 10 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) = $4400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3960 (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 $4400
= 9/100 × 4400
= 9 × 4400/100
= 39600/100 = 396
Thus, simple Interest for 1 year = $396
Now,
∵ If the simple Interest is $396, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/396 years
∴ If the simple Interest is $3960, then the time = 1/396 × 3960 years
= 1 × 3960/396 years
= 3960/396 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(5) 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.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
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(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.
(9) 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.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.