Question:
Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7520
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 = $7520 – $4700 = $2820
Thus, Simple Interest = $2820
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 × 2820/4700 × 6
= 282000/28200
= 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) = $4700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2820 (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 $4700
= 6/100 × 4700
= 6 × 4700/100
= 28200/100 = 282
Thus, simple Interest for 1 year = $282
Now,
∵ If the simple Interest is $282, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/282 years
∴ If the simple Interest is $2820, then the time = 1/282 × 2820 years
= 1 × 2820/282 years
= 2820/282 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
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(10) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?