Question:
Barbara took a loan of $5100 at the rate of 10% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 10% 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 × 10
= 306000/51000
= 6 years (using formula)
Thus, Time (T) = 6 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) = 10% 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 = 10% of Principal
= 10% of $5100
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = 510
Thus, simple Interest for 1 year = $510
Now,
∵ If the simple Interest is $510, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/510 years
∴ If the simple Interest is $3060, then the time = 1/510 × 3060 years
= 1 × 3060/510 years
= 3060/510 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(2) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(6) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(10) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.