Question : Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
Correct Answer 7
Solution & Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7820
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $7820 – $4600 = $3220
Thus, Simple Interest = $3220
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 × 3220/4600 × 10
= 322000/46000
= 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) = $4600
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3220 (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 $3220, then the time = 1/460 × 3220 years
= 1 × 3220/460 years
= 3220/460 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.