Question:
Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12000
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 = $12000 – $6000 = $6000
Thus, Simple Interest = $6000
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 × 6000/6000 × 10
= 600000/60000
= 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) = $6000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6000 (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 $6000
= 10/100 × 6000
= 10 × 6000/100
= 60000/100 = 600
Thus, simple Interest for 1 year = $600
Now,
∵ If the simple Interest is $600, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/600 years
∴ If the simple Interest is $6000, then the time = 1/600 × 6000 years
= 1 × 6000/600 years
= 6000/600 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(8) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.