Question:
Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9520
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 = $9520 – $5600 = $3920
Thus, Simple Interest = $3920
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 × 3920/5600 × 7
= 392000/39200
= 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) = $5600
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3920 (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 = 7% of Principal
= 7% of $5600
= 7/100 × 5600
= 7 × 5600/100
= 39200/100 = 392
Thus, simple Interest for 1 year = $392
Now,
∵ If the simple Interest is $392, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/392 years
∴ If the simple Interest is $3920, then the time = 1/392 × 3920 years
= 1 × 3920/392 years
= 3920/392 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(4) 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.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(6) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(9) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?