Question:
Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8160
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 = $8160 – $5100 = $3060
Thus, Simple Interest = $3060
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 × 3060/5100 × 6
= 306000/30600
= 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) = $5100
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3060 (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 $5100
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = 306
Thus, simple Interest for 1 year = $306
Now,
∵ If the simple Interest is $306, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/306 years
∴ If the simple Interest is $3060, then the time = 1/306 × 3060 years
= 1 × 3060/306 years
= 3060/306 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(3) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.