Question:
Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8280
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 = $8280 – $4600 = $3680
Thus, Simple Interest = $3680
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 × 3680/4600 × 10
= 368000/46000
= 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) = $4600
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3680 (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 $4600
= 10/100 × 4600
= 10 × 4600/100
= 46000/100 = 460
Thus, simple Interest for 1 year = $460
Now,
∵ If the simple Interest is $460, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/460 years
∴ If the simple Interest is $3680, then the time = 1/460 × 3680 years
= 1 × 3680/460 years
= 3680/460 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(3) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
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(7) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
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