Question:
Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12670
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 = $12670 – $7000 = $5670
Thus, Simple Interest = $5670
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 × 5670/7000 × 9
= 567000/63000
= 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) = $7000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5670 (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 $5670, then the time = 1/630 × 5670 years
= 1 × 5670/630 years
= 5670/630 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(2) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(3) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.