Question:
Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10106
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 = $10106 – $6200 = $3906
Thus, Simple Interest = $3906
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 × 3906/6200 × 7
= 390600/43400
= 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) = $6200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3906 (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 $6200
= 7/100 × 6200
= 7 × 6200/100
= 43400/100 = 434
Thus, simple Interest for 1 year = $434
Now,
∵ If the simple Interest is $434, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/434 years
∴ If the simple Interest is $3906, then the time = 1/434 × 3906 years
= 1 × 3906/434 years
= 3906/434 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?
(3) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
(4) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(5) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(8) 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.
(9) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.