Question:
Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9360
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 = $9360 – $6000 = $3360
Thus, Simple Interest = $3360
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 × 3360/6000 × 7
= 336000/42000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3360 (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 $6000
= 7/100 × 6000
= 7 × 6000/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $3360, then the time = 1/420 × 3360 years
= 1 × 3360/420 years
= 3360/420 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(3) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(5) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(9) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?