Question:
Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10640
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 = $10640 – $5600 = $5040
Thus, Simple Interest = $5040
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 × 5040/5600 × 10
= 504000/56000
= 9 years (using formula)
Thus, Time (T) = 9 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) = $5600
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5040 (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 $5600
= 10/100 × 5600
= 10 × 5600/100
= 56000/100 = 560
Thus, simple Interest for 1 year = $560
Now,
∵ If the simple Interest is $560, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/560 years
∴ If the simple Interest is $5040, then the time = 1/560 × 5040 years
= 1 × 5040/560 years
= 5040/560 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(3) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?