Question:
David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7104
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 = $7104 – $4800 = $2304
Thus, Simple Interest = $2304
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 × 2304/4800 × 8
= 230400/38400
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2304 (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 = 8% of Principal
= 8% of $4800
= 8/100 × 4800
= 8 × 4800/100
= 38400/100 = 384
Thus, simple Interest for 1 year = $384
Now,
∵ If the simple Interest is $384, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/384 years
∴ If the simple Interest is $2304, then the time = 1/384 × 2304 years
= 1 × 2304/384 years
= 2304/384 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(5) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(7) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.