Question:
Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12400
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 = $12400 – $6200 = $6200
Thus, Simple Interest = $6200
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 × 6200/6200 × 10
= 620000/62000
= 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) = $6200
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6200 (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 $6200
= 10/100 × 6200
= 10 × 6200/100
= 62000/100 = 620
Thus, simple Interest for 1 year = $620
Now,
∵ If the simple Interest is $620, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/620 years
∴ If the simple Interest is $6200, then the time = 1/620 × 6200 years
= 1 × 6200/620 years
= 6200/620 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 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 7% simple interest.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(4) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(6) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(10) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.