Question:
Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8400
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 = $8400 – $4200 = $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 × 4200/4200 × 10
= 420000/42000
= 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) = $4200
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 $4200
= 10/100 × 4200
= 10 × 4200/100
= 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 $4200, then the time = 1/420 × 4200 years
= 1 × 4200/420 years
= 4200/420 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
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(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
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