Question:
Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11410
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 = $11410 – $7000 = $4410
Thus, Simple Interest = $4410
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 × 4410/7000 × 9
= 441000/63000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $7000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4410 (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 = 9% of Principal
= 9% of $7000
= 9/100 × 7000
= 9 × 7000/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $4410, then the time = 1/630 × 4410 years
= 1 × 4410/630 years
= 4410/630 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(8) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.