Question:
Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6660
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 = $6660 – $4500 = $2160
Thus, Simple Interest = $2160
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 × 2160/4500 × 6
= 216000/27000
= 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) = $4500
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2160 (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 = 6% of Principal
= 6% of $4500
= 6/100 × 4500
= 6 × 4500/100
= 27000/100 = 270
Thus, simple Interest for 1 year = $270
Now,
∵ If the simple Interest is $270, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/270 years
∴ If the simple Interest is $2160, then the time = 1/270 × 2160 years
= 1 × 2160/270 years
= 2160/270 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
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(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
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