Question:
Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10200
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 = $10200 – $6000 = $4200
Thus, Simple Interest = $4200
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 × 4200/6000 × 10
= 420000/60000
= 7 years (using formula)
Thus, Time (T) = 7 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 = $4200 (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 $4200, then the time = 1/600 × 4200 years
= 1 × 4200/600 years
= 4200/600 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.