Question:
Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7344
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 = $7344 – $5400 = $1944
Thus, Simple Interest = $1944
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 × 1944/5400 × 6
= 194400/32400
= 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) = $5400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1944 (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 = 6% of Principal
= 6% of $5400
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = 324
Thus, simple Interest for 1 year = $324
Now,
∵ If the simple Interest is $324, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/324 years
∴ If the simple Interest is $1944, then the time = 1/324 × 1944 years
= 1 × 1944/324 years
= 1944/324 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?